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인기 문제

순위	주제	문제	형식화된 문제
76701	Solve the Differential Equation	(dy)/(dx)=(8x^7)/(6e^y)	$\frac{d y}{d x} = \frac{8 x^{7}}{6 e^{y}}$
76702	Solve the Differential Equation	(ysec(x)^2+sec(x)tan(x))dx+(tan(x)+2y)dy=0	$(y \sec^{2} (x) + \sec (x) \tan (x)) d x + (\tan (x) + 2 y) d y = 0$
76703	Solve the Differential Equation	(dy)/(dx)=(3y)/(x+6)	$\frac{d y}{d x} = \frac{3 y}{x + 6}$
76704	Solve the Differential Equation	(dy)/(dx)-y=cos(x)	$\frac{d y}{d x} - y = \cos (x)$
76705	Solve the Differential Equation	y''''=(x^2)/(y^3)	$y'' = \frac{x^{2}}{y^{3}}$
76706	Solve the Differential Equation	(3xy^2dx+3x^2y+4y^2)dy=0	$(3 x y^{2} d x + 3 x^{2} y + 4 y^{2}) d y = 0$
76707	Solve the Differential Equation	ydx+(1-3y)xdy=3dy	$yd x + (1 - 3 y) x d y = 3 d y$
76708	Solve the Differential Equation	xy''''=2x+3y	$x y'' = 2 x + 3 y$
76709	Solve the Differential Equation	(4+5y)dx+(1+5x)dy=0	$(4 + 5 y) d x + (1 + 5 x) d y = 0$
76710	Solve the Differential Equation	f(x)=e^5	$f (x) = e^{5}$
76711	Solve the Differential Equation	(dy)/(dx) of y=-2x+5	$\frac{d y}{d x}$ of $y = - 2 x + 5$
76712	Solve the Differential Equation	f(x)=(2/(x^5))-5	$f (x) = (\frac{2}{x^{5}}) - 5$
76713	Solve the Differential Equation	x^2y''''-6y=0	$x^{2} y'' - 6 y = 0$
76714	Solve the Differential Equation	(x+1)y''''+(x+2)y=2xe^(-x)	$(x + 1) y'' + (x + 2) y = 2 x e^{- x}$
76715	Solve the Differential Equation	y''''''''-4y''''+20y=0	$y'''' - 4 y'' + 20 y = 0$
76716	Solve the Differential Equation	(dy)/(dx)=xe^(3x)	$\frac{d y}{d x} = x e^{3 x}$
76717	Solve the Differential Equation	(dy)/(dx)=(x^2+x)/(y+5)	$\frac{d y}{d x} = \frac{x^{2} + x}{y + 5}$
76718	Solve the Differential Equation	(dy)/(dx)=3x^(3/8)	$\frac{d y}{d x} = 3 x^{\frac{3}{8}}$
76719	Solve the Differential Equation	1/x(dy)/(dx)+6y=2	$\frac{1}{x} \cdot \frac{d y}{d x} + 6 y = 2$
76720	Solve the Differential Equation	(3x^2y^3+y^4)dx+(3x^3y^2+y^4+4xy^3)dy=0	$(3 x^{2} y^{3} + y^{4}) d x + (3 x^{3} y^{2} + y^{4} + 4 x y^{3}) d y = 0$
76721	Solve the Differential Equation	(x^2+1)(dy)/(dx)-xy=(xy)^2	$(x^{2} + 1) \frac{d y}{d x} - x y = {(x y)}^{2}$
76722	Solve the Differential Equation	(dy)/(dx)=xcos(x)	$\frac{d y}{d x} = x \cos (x)$
76723	Solve the Differential Equation	(dy)/(dx)=8x^(1/2)	$\frac{d y}{d x} = 8 x^{\frac{1}{2}}$
76724	Solve the Differential Equation	xy(dy)/(dx)=x^2-y^2	$x y \frac{d y}{d x} = x^{2} - y^{2}$
76725	Solve the Differential Equation	(dy)/(dt)=4e^(4t)sin(e^(4t)-1296) , y( 6)=0 의 자연로그	$\frac{d y}{d t} = 4 e^{4 t} \sin (e^{4 t} - 1296)$ , $y (\ln (6)) = 0$
76726	Solve the Differential Equation	xy(dy)/(dx)=(x^2+y^2)	$x y \frac{d y}{d x} = (x^{2} + y^{2})$
76727	Solve the Differential Equation	(dy)/(dx)=1/(12 x) , y(1)=0 의 제곱근	$\frac{d y}{d x} = \frac{1}{12 \sqrt{x}}$ , $y (1) = 0$
76728	Solve the Differential Equation	(dy)/(dx)=3x^(-3/4) , y(1)=9	$\frac{d y}{d x} = 3 x^{- \frac{3}{4}}$ , $y (1) = 9$
76729	Solve the Differential Equation	dx+(x-y+6)dy=0	$d x + (x - y + 6) d y = 0$
76730	Solve the Differential Equation	2 xy(dy)/(dx)=3 의 제곱근	$2 \sqrt{x y} \frac{d y}{d x} = 3$
76731	Solve the Differential Equation	y(3+2xy^2)dx+3(x^2y^2+x-1)dy=0	$y (3 + 2 x y^{2}) d x + 3 (x^{2} y^{2} + x - 1) d y = 0$
76732	Solve the Differential Equation	y''''+4/xy=x^3y^3	$y'' + \frac{4}{x} y = x^{3} y^{3}$
76733	Solve the Differential Equation	(d^2y)/(dx^2)-9y=0	$\frac{d^{2} y}{d x^{2}} - 9 y = 0$
76734	Solve the Differential Equation	y(x^3+x^5)dx-x(x^3+y^5)dy=0	$y (x^{3} + x^{5}) d x - x (x^{3} + y^{5}) d y = 0$
76735	Solve the Differential Equation	y''''=7e^x+8x^3+9x^2+1	$y'' = 7 e^{x} + 8 x^{3} + 9 x^{2} + 1$
76736	Solve the Differential Equation	(dy)/(dx)(1+x^2)=-xy	$\frac{d y}{d x} (1 + x^{2}) = - x y$
76737	Solve the Differential Equation	(1+4xy-4x^2y)dx+(x^2-x^3)dy=0	$(1 + 4 x y - 4 x^{2} y) d x + (x^{2} - x^{3}) d y = 0$
76738	Solve the Differential Equation	(x+ y^2-xy)(dy)/(dx)=y 의 제곱근	$(x + \sqrt{y^{2} - x y}) \frac{d y}{d x} = y$
76739	Solve the Differential Equation	(5x^2y+6x^3y^2+4xy^2)dx+(2x^3+3x^4y+3x^2y)dy=0	$(5 x^{2} y + 6 x^{3} y^{2} + 4 x y^{2}) d x + (2 x^{3} + 3 x^{4} y + 3 x^{2} y) d y = 0$
76740	Solve the Differential Equation	(dy)/(dx)=1/( 제곱근 1-x^2)-1/( 제곱근 x)	$\frac{d y}{d x} = \frac{1}{\sqrt{1 - x^{2}}} - \frac{1}{\sqrt{x}}$
76741	Solve the Differential Equation	y''''-3y+e^(3x)=0	$y'' - 3 y + e^{3 x} = 0$
76742	Solve the Differential Equation	y''''=(1-y)cos(x)	$y'' = (1 - y) \cos (x)$
76743	Solve the Differential Equation	x^2ydy-ydx=0	$x^{2} yd y - yd x = 0$
76744	Solve the Differential Equation	(2xsin(y)+y^3e^x)dx+(x^2cos(y)+3y^2e^x)dy=0	$(2 x \sin (y) + y^{3} e^{x}) d x + (x^{2} \cos (y) + 3 y^{2} e^{x}) d y = 0$
76745	Solve the Differential Equation	adb -b^2da=0	adb $- b^{2} d a = 0$
76746	Solve the Differential Equation	f(x)=(x^2)/(x^2-9)	$f (x) = \frac{x^{2}}{x^{2} - 9}$
76747	Solve the Differential Equation	(1+y)dx+(1-x)dy=0	$(1 + y) d x + (1 - x) d y = 0$
76748	Solve the Differential Equation	(dy)/(dx)=3x^2(y+2)	$\frac{d y}{d x} = 3 x^{2} (y + 2)$
76749	Solve the Differential Equation	(dy)/(dt)+2y=1 , y(0)=5/2	$\frac{d y}{d t} + 2 y = 1$ , $y (0) = \frac{5}{2}$
76750	Solve the Differential Equation	(4te^(2x))dy=ye^(2x)dx	$(4 t e^{2 x}) d y = y e^{2 x} d x$
76751	Solve the Differential Equation	(dy)/(dt)=te^y	$\frac{d y}{d t} = t e^{y}$
76752	Solve the Differential Equation	(dP)/(dt)=3100/(1+0.25t)	$\frac{d P}{d t} = \frac{3100}{1 + 0.25 t}$
76753	Solve the Differential Equation	(dy)/(dx)=y''''	$\frac{d y}{d x} = y''$
76754	Solve the Differential Equation	3(x^2+y^2)dx+x(x^2+3y^2+6y)dy=0	$3 (x^{2} + y^{2}) d x + x (x^{2} + 3 y^{2} + 6 y) d y = 0$
76755	Solve the Differential Equation	(dy)/(dx)=tan(x-y)	$\frac{d y}{d x} = \tan (x - y)$
76756	Solve the Differential Equation	(dy)/(dx)=(6x^2)/(9y^2-4) , y(2)=0	$\frac{d y}{d x} = \frac{6 x^{2}}{9 y^{2} - 4}$ , $y (2) = 0$
76757	Solve the Differential Equation	y''''+3y''''+2y=12x^2	$y'' + 3 y'' + 2 y = 12 x^{2}$
76758	Solve the Differential Equation	2(dy)/(dx)=(7x^3)/y	$2 \frac{d y}{d x} = \frac{7 x^{3}}{y}$
76759	Verify the Differential Equation Solution	(dP)/(dt)=4 Pt , P(1)=7 의 제곱근	$\frac{d P}{d t} = 4 \sqrt{P t}$ , $P (1) = 7$
76760	Solve the Differential Equation	xy+y''''=100x	$x y + y'' = 100 x$
76761	Solve the Differential Equation	x^2+y^2+xyy''''=0	$x^{2} + y^{2} + x y y'' = 0$
76762	Solve the Differential Equation	y''''=(x-y+1)^2	$y'' = {(x - y + 1)}^{2}$
76763	Solve the Differential Equation	y''''+ay=b	$y'' + a y = b$
76764	Solve the Differential Equation	y''''''''''''-3y''''-2y=0	$y'''''' - 3 y'' - 2 y = 0$
76765	Solve the Differential Equation	2(yd)x=3xdy	$2 yd x = 3 x d y$
76766	Solve the Differential Equation	(dA)/(dt)=kA	$\frac{d A}{d t} = k A$
76767	Solve the Differential Equation	(dy)/(dx)=2x^(2/3)	$\frac{d y}{d x} = 2 x^{\frac{2}{3}}$
76768	Solve the Differential Equation	(x^3-y^3)dx+xy^2dy=0	$(x^{3} - y^{3}) d x + x y^{2} d y = 0$
76769	Solve the Differential Equation	xy''''-y=x^2cos(x)	$x y'' - y = x^{2} \cos (x)$
76770	Solve the Differential Equation	(dy)/(dx)=1/3 제곱근 ycos( 제곱근 y)^2	$\frac{d y}{d x} = \frac{1}{3} \sqrt{y} \cos^{2} (\sqrt{y})$
76771	Solve the Differential Equation	(x^2+y^2)dy=x(yd)x	$(x^{2} + y^{2}) d y = x yd x$
76772	Solve the Differential Equation	y''''''''-3y''''+4y=0	$y'''' - 3 y'' + 4 y = 0$
76773	Solve the Differential Equation	y^2y''''=x-2	$y^{2} y'' = x - 2$
76774	Solve the Differential Equation	f(x)=(2 2x^2+6x)/3 의 제곱근	$f (x) = \frac{2 \sqrt{2 x^{2} + 6 x}}{3}$
76775	Solve the Differential Equation	sin(xdy)-(yd)x-2sin(xdx)=0	$\sin (x d y) - yd x - 2 \sin (x d x) = 0$
76776	Solve the Differential Equation	(dy)/(dx)-2y=4-x	$\frac{d y}{d x} - 2 y = 4 - x$
76777	Solve the Differential Equation	y''''''''+8y''''=0	$y'''' + 8 y'' = 0$
76778	Solve the Differential Equation	(x^2)/(y^2-3)(dy)/(dx)=1/(2y)	$\frac{x^{2}}{y^{2} - 3} \cdot \frac{d y}{d x} = \frac{1}{2 y}$
76779	Solve the Differential Equation	y(dy)/(dx)=e^x	$y \frac{d y}{d x} = e^{x}$
76780	Solve the Differential Equation	(2 xy-y)dx-xdy=0 의 제곱근	$(2 \sqrt{x y} - y) d x - x d y = 0$
76781	Solve the Differential Equation	(dy)/(dt)=sin(t)+1 , y(pi/3)=1/2	$\frac{d y}{d t} = \sin (t) + 1$ , $y (\frac{π}{3}) = \frac{1}{2}$
76782	Solve the Differential Equation	1/y(dy)/(dt)=41/t	$\frac{1}{y} \cdot \frac{d y}{d t} = 4 \cdot \frac{1}{t}$
76783	Solve the Differential Equation	(dy)/(dx)+1/xy=e^x	$\frac{d y}{d x} + \frac{1}{x} y = e^{x}$
76784	Solve the Differential Equation	sin(y)(x+sin(y))dx+2x^2cos(ydy)=0	$\sin (y) (x + \sin (y)) d x + 2 x^{2} \cos (yd y) = 0$
76785	Solve the Differential Equation	(dy)/(dx)-(2y)/(x+1)=(x+1)^2	$\frac{d y}{d x} - \frac{2 y}{x + 1} = {(x + 1)}^{2}$
76786	Solve the Differential Equation	x(yd)x+y^2dy=0	$x yd x + y^{2} d y = 0$
76787	Solve the Differential Equation	f(x)=2cos(x)^2	$f (x) = 2 \cos^{2} (x)$
76788	Solve the Differential Equation	(dy)/(dx)=x^5y	$\frac{d y}{d x} = x^{5} y$
76789	Solve the Differential Equation	(dy)/(dx)=4y^2sec(2x)^2 and y(pi/8)=1	$\frac{d y}{d x} = 4 y^{2} \sec^{2} (2 x)$ and $y (\frac{π}{8}) = 1$
76790	Solve the Differential Equation	(ds)/(dt)=-5t+cos(t) , s(0)=-1	$\frac{d s}{d t} = - 5 t + \cos (t)$ , $s (0) = - 1$
76791	Solve the Differential Equation	(x+1)y''''-xy=x+x^2	$(x + 1) y'' - x y = x + x^{2}$
76792	Solve the Differential Equation	(dy)/(dx)=(3x)/(2y)	$\frac{d y}{d x} = \frac{3 x}{2 y}$
76793	Solve the Differential Equation	(dy)/(dx)+y=x ; ; , y(0)=4	$\frac{d y}{d x} + y = x$ ; ; , $y (0) = 4$
76794	Solve the Differential Equation	(dx)/(dt)=3e^t-7 , x(0)=1	$\frac{d x}{d t} = 3 e^{t} - 7$ , $x (0) = 1$
76795	Solve the Differential Equation	(dy)/(dx)=(2x+1)/(2y) , y(-2)=-1	$\frac{d y}{d x} = \frac{(2 x + 1)}{2 y}$ , $y (- 2) = - 1$
76796	Solve the Differential Equation	xe^(-t)(dx)/(dt)=t , x(0)=1	$x e^{- t} \frac{d x}{d t} = t$ , $x (0) = 1$
76797	Solve the Differential Equation	(dy)/(dx)=x^2(2y-3)^2	$\frac{d y}{d x} = x^{2} {(2 y - 3)}^{2}$
76798	Solve the Differential Equation	(x^5-y^2)dx=-2x(yd)y	$(x^{5} - y^{2}) d x = - 2 x yd y$
76799	Solve the Differential Equation	(dy)/(dx)=(y^2)/(1-x) , y(0)=1	$\frac{d y}{d x} = \frac{y^{2}}{1 - x}$ , $y (0) = 1$
76800	Solve the Differential Equation	(dy)/(dx)=( 제곱근 x)/( 제곱근 y)	$\frac{d y}{d x} = \frac{\sqrt{x}}{\sqrt{y}}$