Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
71701	Solve the Differential Equation	(x+y)dx-(x+y+3)dy=0	$(x + y) d x - (x + y + 3) d y = 0$
71702	Solve the Differential Equation	e^xe^ydx-e^(-2y)dy=0	$e^{x} e^{y} d x - e^{- 2 y} d y = 0$
71703	Solve the Differential Equation	y''''''''+y=sec(x)	$y'''' + y = \sec (x)$
71704	Solve the Differential Equation	(dy)/(dx)=(2y^4+x^4)/(xy^3)	$\frac{d y}{d x} = \frac{2 y^{4} + x^{4}}{x y^{3}}$
71705	Solve the Differential Equation	sin(theta)(dr)/(dtheta)+(cos(theta))r=tan(theta)	$\sin (θ) \frac{d r}{d θ} + (\cos (θ)) r = \tan (θ)$
71706	Solve the Differential Equation	(y- square root of x^2+y^2)dx-xdy=0	$(y - \sqrt{x^{2} + y^{2}}) d x - x d y = 0$
71707	Solve the Differential Equation	2y(x+1)dy=xdx	$2 y (x + 1) d y = x d x$
71708	Solve the Differential Equation	(dy)/(dx)=5x^4y	$\frac{d y}{d x} = 5 x^{4} y$
71709	Solve the Differential Equation	(dy)/(dx)-x^2y^2=x^2	$\frac{d y}{d x} - x^{2} y^{2} = x^{2}$
71710	Solve the Differential Equation	(dy)/(dx)=x+y+2	$\frac{d y}{d x} = x + y + 2$
71711	Solve the Differential Equation	(dy)/(dx)=x^3	$\frac{d y}{d x} = x^{3}$
71712	Solve the Differential Equation	3y(x^2-1)dx+(x^3+8y-3x)dy=0	$3 y (x^{2} - 1) d x + (x^{3} + 8 y - 3 x) d y = 0$
71713	Solve the Differential Equation	x(dy)/(dx)+y=xy^3	$x \frac{d y}{d x} + y = x y^{3}$
71714	Solve the Differential Equation	y''''+100y=0	$y'' + 100 y = 0$
71715	Solve the Differential Equation	(dy)/(dx)-4/xy=x^4	$\frac{d y}{d x} - \frac{4}{x} y = x^{4}$
71716	Solve the Differential Equation	(dy)/(dx)-yx=x	$\frac{d y}{d x} - y x = x$
71717	Solve the Differential Equation	t(dy)/(dx)=6te^(2t)+x(2t-1)	$t \frac{d y}{d x} = 6 t e^{2 t} + x (2 t - 1)$
71718	Solve the Differential Equation	10y''''''''+y=3	$10 y'''' + y = 3$
71719	Solve the Differential Equation	(dy)/(dx)=8x^7y	$\frac{d y}{d x} = 8 x^{7} y$
71720	Solve the Differential Equation	2y''''-y''''''''=0	$2 y'' - y'''' = 0$
71721	Solve the Differential Equation	(dy)/(dx)=2xy^-2	$\frac{d y}{d x} = 2 x y^{- 2}$
71722	Solve the Differential Equation	(dy)/(dx)=(x^3-2y)/x	$\frac{d y}{d x} = \frac{x^{3} - 2 y}{x}$
71723	Solve the Differential Equation	y''''=4y	$y'' = 4 y$
71724	Solve the Differential Equation	y''''''''-36y=0	$y'''' - 36 y = 0$
71725	Solve the Differential Equation	y''''+2xy=x^3	$y'' + 2 x y = x^{3}$
71726	Solve the Differential Equation	y''''+2/xy=0	$y'' + \frac{2}{x} y = 0$
71727	Solve the Differential Equation	(dy)/(dt)=(3t^2)/y	$\frac{d y}{d t} = \frac{3 t^{2}}{y}$
71728	Verify the Differential Equation Solution	y=2e^(3x)-5e^(4x) , (d^2y)/(dx^2)-7(dy)/(dx)+12y=0	$y = 2 e^{3 x} - 5 e^{4 x}$ , $\frac{d^{2} y}{d x^{2}} - 7 \frac{d y}{d x} + 12 y = 0$
71729	Solve the Differential Equation	(dy)/(dx)=13x^12y	$\frac{d y}{d x} = 13 x^{12} y$
71730	Solve the Differential Equation	(dy)/(dx)=6x-5	$\frac{d y}{d x} = 6 x - 5$
71731	Solve the Differential Equation	y''''=(2xy)/(1+x^2)	$y'' = \frac{2 x y}{1 + x^{2}}$
71732	Solve the Differential Equation	(dy)/(dx)=(8e^(4x))/(2cos(2y))	$\frac{d y}{d x} = \frac{8 e^{4 x}}{2 \cos (2 y)}$
71733	Solve the Differential Equation	(dy)/(dx)=(x^2+2)/(3y^2)	$\frac{d y}{d x} = \frac{x^{2} + 2}{3 y^{2}}$
71734	Solve the Differential Equation	(dy)/(dt)+y^2t=t	$\frac{d y}{d t} + y^{2} t = t$
71735	Solve the Differential Equation	(dy)/(dx)+2/xy=6x^3	$\frac{d y}{d x} + \frac{2}{x} y = 6 x^{3}$
71736	Solve the Differential Equation	y''''=y/(2x)	$y'' = \frac{y}{2 x}$
71737	Solve the Differential Equation	y''''-y''''=0	$y'' - y'' = 0$
71738	Verify the Existence and Uniqueness of Solutions for the Differential Equation	(dy)/(dx) = square root of x-y , (3,1)	$\frac{d y}{d x} = \sqrt{x - y}$ , $(3, 1)$
71739	Solve the Differential Equation	(x^2-3y^2)dx+2x(yd)y=0	$(x^{2} - 3 y^{2}) d x + 2 x yd y = 0$
71740	Solve the Differential Equation	x(dy)/(dx)+3y=2x^5	$x \frac{d y}{d x} + 3 y = 2 x^{5}$
71741	Solve the Differential Equation	(dy)/(dx)=xy+x-y-1 , y(0)=1	$\frac{d y}{d x} = x y + x - y - 1$ , $y (0) = 1$
71742	Solve the Differential Equation	(dy)/(dx)+y=x+1	$\frac{d y}{d x} + y = x + 1$
71743	Solve the Differential Equation	(dy)/(dx)=2y-1	$\frac{d y}{d x} = 2 y - 1$
71744	Solve the Differential Equation	2y''''''''''''-7y''''''''+12y''''+8y=0	$2 y'''''' - 7 y'''' + 12 y'' + 8 y = 0$
71745	Solve the Differential Equation	y''''''''''''-y=0	$y'''''' - y = 0$
71746	Solve the Differential Equation	(dy)/(dx)=13xy	$\frac{d y}{d x} = 13 x y$
71747	Solve the Differential Equation	x(dy)/(dx)=x^2+3y	$x \frac{d y}{d x} = x^{2} + 3 y$
71748	Solve the Differential Equation	(dy)/(dt)=(t^2 square root of y)/(1+t^3)	$\frac{d y}{d t} = \frac{t^{2} \sqrt{y}}{1 + t^{3}}$
71749	Solve the Differential Equation	f(x)=3x^3-2x+6	$f (x) = 3 x^{3} - 2 x + 6$
71750	Solve the Differential Equation	(dy)/(dx)=y^2x^3	$\frac{d y}{d x} = y^{2} x^{3}$
71751	Solve the Differential Equation	xy^2(dy)/(dx)-x=1	$x y^{2} \frac{d y}{d x} - x = 1$
71752	Solve the Differential Equation	(dy)/(dx)=xy+2x	$\frac{d y}{d x} = x y + 2 x$
71753	Solve the Differential Equation	y''''''''''''+y''''=0	$y'''''' + y'' = 0$
71754	Solve the Differential Equation	x(dy)/(dx)+y=2x	$x \frac{d y}{d x} + y = 2 x$
71755	Solve the Differential Equation	(3x-1)y''''=6y-10(3x-1)^(1/3)	$(3 x - 1) y'' = 6 y - 10 {(3 x - 1)}^{\frac{1}{3}}$
71756	Solve the Differential Equation	(dy)/(dx)=1/(e^y-x)	$\frac{d y}{d x} = \frac{1}{e^{y} - x}$
71757	Solve the Differential Equation	(x^2-y^2)dx+x(yd)y=0	$(x^{2} - y^{2}) d x + x yd y = 0$
71758	Solve the Differential Equation	(dy)/(dx)=2x(1+y^2)	$\frac{d y}{d x} = 2 x (1 + y^{2})$
71759	Solve the Differential Equation	(dy)/(dx)=(3(y-2))/x	$\frac{d y}{d x} = \frac{3 (y - 2)}{x}$
71760	Solve the Differential Equation	(dy)/(dx)=6xy^8	$\frac{d y}{d x} = 6 x y^{8}$
71761	Solve the Differential Equation	(dy)/(dx)=x(1-2y)	$\frac{d y}{d x} = x (1 - 2 y)$
71762	Solve the Differential Equation	(3x+2y)dx+(2x+y)dy=0	$(3 x + 2 y) d x + (2 x + y) d y = 0$
71763	Solve the Differential Equation	xy^2dy-x^2(yd)x=0	$x y^{2} d y - x^{2} yd x = 0$
71764	Solve the Differential Equation	(dp)/(dt)=7 square root of pt	$\frac{d p}{d t} = 7 \sqrt{p t}$
71765	Solve the Differential Equation	(dy)/(dx)=(x+1)(x+2)	$\frac{d y}{d x} = (x + 1) (x + 2)$
71766	Solve the Differential Equation	(2+x)dy=3(yd)x	$(2 + x) d y = 3 yd x$
71767	Solve the Differential Equation	(dy)/(dx)+3/xy=( natural log of x)/(x^2)	$\frac{d y}{d x} + \frac{3}{x} y = \frac{\ln (x)}{x^{2}}$
71768	Solve the Differential Equation	(dy)/(dx)=xy-y	$\frac{d y}{d x} = x y - y$
71769	Solve the Differential Equation	2x(yd)x-(1+x^2)dy=0	$2 x yd x - (1 + x^{2}) d y = 0$
71770	Solve the Differential Equation	(dy)/(dx)=xe^(6x-5y)	$\frac{d y}{d x} = x e^{6 x - 5 y}$
71771	Solve the Differential Equation	(2+x)(dy)/(dx)=3y	$(2 + x) \frac{d y}{d x} = 3 y$
71772	Solve the Differential Equation	3y''''''''+y=0	$3 y'''' + y = 0$
71773	Solve the Differential Equation	(dx)/(dy)=(y^2)/(1+x)	$\frac{d x}{d y} = \frac{y^{2}}{1 + x}$
71774	Solve the Differential Equation	(dy)/(dx)=((xy)^2)/8+y^2	$\frac{d y}{d x} = \frac{{(x y)}^{2}}{8} + y^{2}$
71775	Solve the Differential Equation	(dy)/(dx)-y/x=y^9	$\frac{d y}{d x} - \frac{y}{x} = y^{9}$
71776	Solve the Differential Equation	(dy)/(dx)=y^2-(xy)^2	$\frac{d y}{d x} = y^{2} - {(x y)}^{2}$
71777	Solve the Differential Equation	(x^2+y)dx+(y^3+x)dy=0	$(x^{2} + y) d x + (y^{3} + x) d y = 0$
71778	Solve the Differential Equation	(dy)/(dx)=(-x)/y , y(3)=4	$\frac{d y}{d x} = \frac{- x}{y}$ , $y (3) = 4$
71779	Solve the Differential Equation	(dy)/(dx)=-xe^y	$\frac{d y}{d x} = - x e^{y}$
71780	Solve the Differential Equation	(2xy^2+3x^2)dx+(2x^2y+4y^3)dy=0	$(2 x y^{2} + 3 x^{2}) d x + (2 x^{2} y + 4 y^{3}) d y = 0$
71781	Solve the Differential Equation	(2dy)/(dx)=(y(x+1))/x	$\frac{2 d y}{d x} = \frac{y (x + 1)}{x}$
71782	Solve the Differential Equation	(dy)/(dx)=(xy)/(x^2+1)	$\frac{d y}{d x} = \frac{x y}{x^{2} + 1}$
71783	Solve the Differential Equation	e^(2x-y)dx+e^(y-2x)dy=0	$e^{2 x - y} d x + e^{y - 2 x} d y = 0$
71784	Solve the Differential Equation	(du)/(dt)=(4+t^4)/(ut^2+u^4t^2)	$\frac{d u}{d t} = \frac{4 + t^{4}}{u t^{2} + u^{4} t^{2}}$
71785	Solve the Differential Equation	y''''''''''''-3y''''+2y=0	$y'''''' - 3 y'' + 2 y = 0$
71786	Solve the Differential Equation	(x+y-1)dx+(2x+2y+1)dy=0	$(x + y - 1) d x + (2 x + 2 y + 1) d y = 0$
71787	Solve the Differential Equation	(dy)/(dx)+3y=8	$\frac{d y}{d x} + 3 y = 8$
71788	Solve the Differential Equation	2y^4+3y''''''''''''+2y''''''''+6y''''-4y=0	$2 y^{4} + 3 y'''''' + 2 y'''' + 6 y'' - 4 y = 0$
71789	Solve the Differential Equation	(dy)/(dx)=6x^5 square root of y-1	$\frac{d y}{d x} = 6 x^{5} \sqrt{y - 1}$
71790	Solve the Differential Equation	(dy)/(dx)=42x	$\frac{d y}{d x} = 42 x$
71791	Solve the Differential Equation	vdx+(2x+1-vx)dv=0	$v d x + (2 x + 1 - v x) d v = 0$
71792	Solve the Differential Equation	(dy)/(dx)=4x^3+6x^2-2x+1	$\frac{d y}{d x} = 4 x^{3} + 6 x^{2} - 2 x + 1$
71793	Solve the Differential Equation	y''''''''+y=sec(x)^2	$y'''' + y = \sec^{2} (x)$
71794	Solve the Differential Equation	(dy)/(dx)=1/(x^2)	$\frac{d y}{d x} = \frac{1}{x^{2}}$
71795	Solve the Differential Equation	(dy)/(dx)=-x^2y^2	$\frac{d y}{d x} = - x^{2} y^{2}$
71796	Solve the Differential Equation	xy''''-2y=2x^3	$x y'' - 2 y = 2 x^{3}$
71797	Solve the Differential Equation	y''''+y''''=0	$y'' + y'' = 0$
71798	Solve the Differential Equation	x^2dx=3y^2dy	$x^{2} d x = 3 y^{2} d y$
71799	Solve the Differential Equation	5 square root of xy(dy)/(dx)=4	$5 \sqrt{x y} \frac{d y}{d x} = 4$
71800	Solve the Differential Equation	(10-6y+e^(-3x))dx-2dy=0	$(10 - 6 y + e^{- 3 x}) d x - 2 d y = 0$