Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
71801	Solve the Differential Equation	(ds)/(dt)=cos(t)-sin(t) , s(pi/2)=3	$\frac{d s}{d t} = \cos (t) - \sin (t)$ , $s (\frac{π}{2}) = 3$
71802	Solve the Differential Equation	(dy)/(dx)=3xe^y , y(0)=0	$\frac{d y}{d x} = 3 x e^{y}$ , $y (0) = 0$
71803	Solve the Differential Equation	(y-2)dx+(3x-y)dy=0	$(y - 2) d x + (3 x - y) d y = 0$
71804	Solve the Differential Equation	(dy)/(dx)=(1+2x) square root of y	$\frac{d y}{d x} = (1 + 2 x) \sqrt{y}$
71805	Solve the Differential Equation	(dy)/(dx)=(11x)/y	$\frac{d y}{d x} = \frac{11 x}{y}$
71806	Solve the Differential Equation	y''''=2x-y	$y'' = 2 x - y$
71807	Solve the Differential Equation	(dy)/(dx)=yx^2	$\frac{d y}{d x} = y x^{2}$
71808	Solve the Differential Equation	(x-y)dx+(x-y+1)dy=0	$(x - y) d x + (x - y + 1) d y = 0$
71809	Solve the Differential Equation	y''''=x^3	$y'' = x^{3}$
71810	Solve the Differential Equation	(dy)/(dx)=10e^(x-y)	$\frac{d y}{d x} = 10 e^{x - y}$
71811	Solve the Differential Equation	ydx+xdy=0	$yd x + x d y = 0$
71812	Solve the Differential Equation	(x+2y+1)dx+(2x-y-1)dy=0	$(x + 2 y + 1) d x + (2 x - y - 1) d y = 0$
71813	Solve the Differential Equation	(dy)/(dx)-y/x=x	$\frac{d y}{d x} - \frac{y}{x} = x$
71814	Solve the Differential Equation	(dy)/(dx)=e^(2x-y)	$\frac{d y}{d x} = e^{2 x - y}$
71815	Solve the Differential Equation	(dy)/(dx)=(3x)/(4y)	$\frac{d y}{d x} = \frac{3 x}{4 y}$
71816	Solve the Differential Equation	y''''+y=x	$y'' + y = x$
71817	Solve the Differential Equation	(dy)/(dx)=2x-3 , y(1)=4	$\frac{d y}{d x} = 2 x - 3$ , $y (1) = 4$
71818	Solve the Differential Equation	f(x)=x^3	$f (x) = x^{3}$
71819	Solve the Differential Equation	y''''+7xe^y=0	$y'' + 7 x e^{y} = 0$
71820	Solve the Differential Equation	(x+x^2y)dy=(2x+xy^2)dx	$(x + x^{2} y) d y = (2 x + x y^{2}) d x$
71821	Solve the Differential Equation	y(y^3-x)dx+x(y^3+x)dy=0	$y (y^{3} - x) d x + x (y^{3} + x) d y = 0$
71822	Solve the Differential Equation	(dy)/(dx)+2y=3	$\frac{d y}{d x} + 2 y = 3$
71823	Solve the Differential Equation	(2x+y)dx+(x-2y)dy=0	$(2 x + y) d x + (x - 2 y) d y = 0$
71824	Solve the Differential Equation	(dy)/(dx)=6x-7	$\frac{d y}{d x} = 6 x - 7$
71825	Solve the Differential Equation	2x(yd)x+y^2dy=0	$2 x yd x + y^{2} d y = 0$
71826	Solve the Differential Equation	(du)/(dt)=(6+t^4)/(ut^2+u^4t^2)	$\frac{d u}{d t} = \frac{6 + t^{4}}{u t^{2} + u^{4} t^{2}}$
71827	Solve the Differential Equation	(dy)/(dx)=2y+2x	$\frac{d y}{d x} = 2 y + 2 x$
71828	Solve the Differential Equation	x(dy)/(dx)+y=0	$x \frac{d y}{d x} + y = 0$
71829	Solve the Differential Equation	(dy)/(dx)=1/( square root of 16-x^2) , y(0)=pi	$\frac{d y}{d x} = \frac{1}{\sqrt{16 - x^{2}}}$ , $y (0) = π$
71830	Solve the Differential Equation	(dy)/(dx)+y=y^2	$\frac{d y}{d x} + y = y^{2}$
71831	Solve the Differential Equation	(dy)/(dx)=e^(-y)(2x-4)	$\frac{d y}{d x} = e^{- y} (2 x - 4)$
71832	Solve the Differential Equation	x(dy)/(dx)=y+x^3+3x^2-2x	$x \frac{d y}{d x} = y + x^{3} + 3 x^{2} - 2 x$
71833	Solve the Differential Equation	(dy)/(dx)=7x^6y	$\frac{d y}{d x} = 7 x^{6} y$
71834	Solve the Differential Equation	y''''+4y=1.4	$y'' + 4 y = 1.4$
71835	Solve the Differential Equation	f(x)=x^2sin(x)	$f (x) = x^{2} \sin (x)$
71836	Solve the Differential Equation	2(yd)x=(x^2+4)dy	$2 yd x = (x^{2} + 4) d y$
71837	Solve the Differential Equation	(y-cos(x)^2)dx+cos(xdy)=0	$(y - \cos^{2} (x)) d x + \cos (x d y) = 0$
71838	Solve the Differential Equation	(dy)/(dx)+y/x=x^6	$\frac{d y}{d x} + \frac{y}{x} = x^{6}$
71839	Solve the Differential Equation	(dp)/(dt)=t^2p-p+t^2-1	$\frac{d p}{d t} = t^{2} p - p + t^{2} - 1$
71840	Solve the Differential Equation	(dy)/(dx)=x^3y	$\frac{d y}{d x} = x^{3} y$
71841	Solve the Differential Equation	(dy)/(dx)=sec(x)^2	$\frac{d y}{d x} = \sec^{2} (x)$
71842	Solve the Differential Equation	y''''=3x^2y	$y'' = 3 x^{2} y$
71843	Solve the Differential Equation	y''''=4x^3	$y'' = 4 x^{3}$
71844	Solve the Differential Equation	(dy)/(dx)=(x^2)/(cos(y))	$\frac{d y}{d x} = \frac{x^{2}}{\cos (y)}$
71845	Solve the Differential Equation	(1+x^2)y''''+xy=x^-1(1+x^2)^(1/2)	$(1 + x^{2}) y'' + x y = x^{- 1} {(1 + x^{2})}^{\frac{1}{2}}$
71846	Solve the Differential Equation	(dy)/(dx)=4sin(2x)	$\frac{d y}{d x} = 4 \sin (2 x)$
71847	Solve the Differential Equation	(dy)/(dt)=3y	$\frac{d y}{d t} = 3 y$
71848	Solve the Differential Equation	y''''''''+y=sin(x)	$y'''' + y = \sin (x)$
71849	Solve the Differential Equation	(dy)/(dx)=4x+2 , y(0)=1	$\frac{d y}{d x} = 4 x + 2$ , $y (0) = 1$
71850	Solve the Differential Equation	(dP)/(dt)=2 square root of Pt	$\frac{d P}{d t} = 2 \sqrt{P t}$
71851	Solve the Differential Equation	(dy)/(dx)+3y=3x^2e^(-3x)	$\frac{d y}{d x} + 3 y = 3 x^{2} e^{- 3 x}$
71852	Solve the Differential Equation	y''''''''+2y''''+2y=0	$y'''' + 2 y'' + 2 y = 0$
71853	Solve the Differential Equation	(dP)/(dx)=0	$\frac{d P}{d x} = 0$
71854	Solve the Differential Equation	xy''''+y^2=0	$x y'' + y^{2} = 0$
71855	Solve the Differential Equation	y''''''''''''-5y''''''''+3y''''+9y=0	$y'''''' - 5 y'''' + 3 y'' + 9 y = 0$
71856	Solve the Differential Equation	(dy)/(dx)=y+x	$\frac{d y}{d x} = y + x$
71857	Solve the Differential Equation	y''''-6y''''+13y=0	$y'' - 6 y'' + 13 y = 0$
71858	Solve the Differential Equation	(dy)/(dx)=-2x+15x^2	$\frac{d y}{d x} = - 2 x + 15 x^{2}$
71859	Solve the Differential Equation	(dy)/(dx)=1/( square root of 36-x^2) , y(0)=pi	$\frac{d y}{d x} = \frac{1}{\sqrt{36 - x^{2}}}$ , $y (0) = π$
71860	Solve the Differential Equation	(dy)/(dx)+8x^3=9x^2	$\frac{d y}{d x} + 8 x^{3} = 9 x^{2}$
71861	Solve the Differential Equation	(dy)/(dx)=14xy	$\frac{d y}{d x} = 14 x y$
71862	Solve the Differential Equation	(dx)/(dt)=3xt^2	$\frac{d x}{d t} = 3 x t^{2}$
71863	Solve the Differential Equation	(6x+y^2)dx+y(2x-3)dy=0	$(6 x + y^{2}) d x + y (2 x - 3) d y = 0$
71864	Solve the Differential Equation	(dy)/(dx)=-6y	$\frac{d y}{d x} = - 6 y$
71865	Solve the Differential Equation	(y^2+2xy)dx-x^2dy=0	$(y^{2} + 2 x y) d x - x^{2} d y = 0$
71866	Solve the Differential Equation	y'''' = square root of 3x+4	$y'' = \sqrt{3 x + 4}$
71867	Solve the Differential Equation	(dy)/(dt)=y	$\frac{d y}{d t} = y$
71868	Solve the Differential Equation	xy^2dy=(x^3+y^3)dx	$x y^{2} d y = (x^{3} + y^{3}) d x$
71869	Solve the Differential Equation	f(x)=3x^2+5x-6	$f (x) = 3 x^{2} + 5 x - 6$
71870	Solve the Differential Equation	(x+2y-1)dx+3(x+2y)dy=0	$(x + 2 y - 1) d x + 3 (x + 2 y) d y = 0$
71871	Solve the Differential Equation	(dy)/(dx)sin(x)+ycos(x)=1	$\frac{d y}{d x} \sin (x) + y \cos (x) = 1$
71872	Solve the Differential Equation	(d^3x)/(dt^3)-19(dx)/(dt)+30=0	$\frac{d^{3} x}{d t^{3}} - 19 \frac{d x}{d t} + 30 = 0$
71873	Solve the Differential Equation	(dy)/(dx)=e^(0.5x)	$\frac{d y}{d x} = e^{0.5 x}$
71874	Solve the Differential Equation	(dy)/(dx)=7xe^y	$\frac{d y}{d x} = 7 x e^{y}$
71875	Solve the Differential Equation	(dy)/(dt)=t^2-y^2	$\frac{d y}{d t} = t^{2} - y^{2}$
71876	Solve the Differential Equation	(dy)/(dx)=(e^y)/(x^2)	$\frac{d y}{d x} = \frac{e^{y}}{x^{2}}$
71877	Solve the Differential Equation	(dy)/(dx)-y=2x	$\frac{d y}{d x} - y = 2 x$
71878	Solve the Differential Equation	xy''''+y''''=0	$x y'' + y'' = 0$
71879	Solve the Differential Equation	(x^3+y^3)dx-xy^2dy=0	$(x^{3} + y^{3}) d x - x y^{2} d y = 0$
71880	Solve the Differential Equation	xy''''=x+y	$x y'' = x + y$
71881	Solve the Differential Equation	(dy)/(dx)=(x^2)/(6e^y)	$\frac{d y}{d x} = \frac{x^{2}}{6 e^{y}}$
71882	Solve the Differential Equation	4/tdt-(y-3)/ydy=0	$\frac{4}{t} d t - \frac{y - 3}{y} d y = 0$
71883	Solve the Differential Equation	(dy)/(dt)+3y=13sin(2t) , y(0)=6	$\frac{d y}{d t} + 3 y = 13 \sin (2 t)$ , $y (0) = 6$
71884	Solve the Differential Equation	(ds)/(dt)=cos(t)-sin(t) , s(pi/2)=7	$\frac{d s}{d t} = \cos (t) - \sin (t)$ , $s (\frac{π}{2}) = 7$
71885	Solve the Differential Equation	(-3x+y-1)dx+(x+y+3)dy=0	$(- 3 x + y - 1) d x + (x + y + 3) d y = 0$
71886	Solve the Differential Equation	(dy)/(dx)=xe^(-y)+10e^(-y)	$\frac{d y}{d x} = x e^{- y} + 10 e^{- y}$
71887	Solve the Differential Equation	(dy)/(dx)=2sin(x)	$\frac{d y}{d x} = 2 \sin (x)$
71888	Solve the Differential Equation	(xcsc(y/x)-y)dx+xdy=0	$(x \csc (\frac{y}{x}) - y) d x + x d y = 0$
71889	Solve the Differential Equation	2xyy''''=y^2-2x^3	$2 x y y'' = y^{2} - 2 x^{3}$
71890	Solve the Differential Equation	(dy)/(dx)+ytan(x)=sec(x)	$\frac{d y}{d x} + y \tan (x) = \sec (x)$
71891	Solve the Differential Equation	(dy)/(dx)=(1-x^2)/(y^2)	$\frac{d y}{d x} = \frac{1 - x^{2}}{y^{2}}$
71892	Solve the Differential Equation	(dy)/(dx)=1+x+y^2+xy^2	$\frac{d y}{d x} = 1 + x + y^{2} + x y^{2}$
71893	Solve the Differential Equation	y''''+3y=6x+11	$y'' + 3 y = 6 x + 11$
71894	Solve the Differential Equation	y''''=-4y	$y'' = - 4 y$
71895	Solve the Differential Equation	general solution (x-2y)dx+2(y-x)dy=0	general solution $(x - 2 y) d x + 2 (y - x) d y = 0$
71896	Solve the Differential Equation	(dy)/(dx)=e^xy^2	$\frac{d y}{d x} = e^{x} y^{2}$
71897	Solve the Differential Equation	y''''+y=sin(x)	$y'' + y = \sin (x)$
71898	Solve the Differential Equation	y''''+2y=e^t	$y'' + 2 y = e^{t}$
71899	Solve the Differential Equation	(dz)/(dt)-1/(2t)z=0	$\frac{d z}{d t} - \frac{1}{2 t} z = 0$
71900	Solve the Differential Equation	2xy(dy)/(dx)=x^2+y^2	$2 x y \frac{d y}{d x} = x^{2} + y^{2}$