Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
73601	Solve the Differential Equation	xy''''+1=0	$x y'' + 1 = 0$
73602	Solve the Differential Equation	y''''=3y+2	$y'' = 3 y + 2$
73603	Solve the Differential Equation	y''''=-2x^3+12x^2-20x+8.5	$y'' = - 2 x^{3} + 12 x^{2} - 20 x + 8.5$
73604	Solve the Differential Equation	(y^3+kxy^4-2x)dx+(3xy^2+20x^2y^3)dy=0	$(y^{3} + k x y^{4} - 2 x) d x + (3 x y^{2} + 20 x^{2} y^{3}) d y = 0$
73605	Solve the Differential Equation	(x^2y^5+y^3)dx+(x^3y^4+x)dy=0	$(x^{2} y^{5} + y^{3}) d x + (x^{3} y^{4} + x) d y = 0$
73606	Solve the Differential Equation	(dv)/(dt)+2v=t	$\frac{d v}{d t} + 2 v = t$
73607	Solve the Differential Equation	(dx)/(dt)=20-(8x)/200	$\frac{d x}{d t} = 20 - \frac{8 x}{200}$
73608	Solve the Differential Equation	(d^2y)/(dx^2)-4(dy)/(dx)+5y=0	$\frac{d^{2} y}{d x^{2}} - 4 \frac{d y}{d x} + 5 y = 0$
73609	Solve the Differential Equation	(dy)/(dx)=(x(y^2+1)^4)/(y(x+2))	$\frac{d y}{d x} = \frac{x {(y^{2} + 1)}^{4}}{y (x + 2)}$
73610	Solve the Differential Equation	(dy)/(dx)=(x+1)	$\frac{d y}{d x} = (x + 1)$
73611	Solve the Differential Equation	(dy)/(dx)=28x	$\frac{d y}{d x} = 28 x$
73612	Solve the Differential Equation	y''''+2y=4x	$y'' + 2 y = 4 x$
73613	Solve the Differential Equation	(x-1)y''''+2y''''=0	$(x - 1) y'' + 2 y'' = 0$
73614	Solve the Differential Equation	(dy)/(dx)=-x/y , y(3)=4	$\frac{d y}{d x} = - \frac{x}{y}$ , $y (3) = 4$
73615	Solve the Differential Equation	(dy)/(dx)=(8x)/(7y)	$\frac{d y}{d x} = \frac{8 x}{7 y}$
73616	Solve the Differential Equation	(dy)/(dx)=e^(5x+2y)	$\frac{d y}{d x} = e^{5 x + 2 y}$
73617	Solve the Differential Equation	(x+2y-1)dx-(2x+y-5)dy=0	$(x + 2 y - 1) d x - (2 x + y - 5) d y = 0$
73618	Solve the Differential Equation	Solve (dy)/(x^2)=3y^2dx	Solve $\frac{d y}{x^{2}} = 3 y^{2} d x$
73619	Solve the Differential Equation	(x+3x^3sin(y))dx+x^4cos(ydy)=0	$(x + 3 x^{3} \sin (y)) d x + x^{4} \cos (yd y) = 0$
73620	Solve the Differential Equation	dx+(x-y^2)dy=0	$d x + (x - y^{2}) d y = 0$
73621	Solve the Differential Equation	x(dy)/(dx)+y=xe^x	$x \frac{d y}{d x} + y = x e^{x}$
73622	Solve the Differential Equation	(dtheta)/(dt)=g/ltheta	$\frac{d θ}{d t} = \frac{g}{l} θ$
73623	Solve the Differential Equation	xy''''=2y+x^2	$x y'' = 2 y + x^{2}$
73624	Solve the Differential Equation	(d^2y)/(dx^2)=e^x	$\frac{d^{2} y}{d x^{2}} = e^{x}$
73625	Solve the Differential Equation	(dy)/(dx)=tan(x)cos(y)^2	$\frac{d y}{d x} = \tan (x) \cos^{2} (y)$
73626	Solve the Differential Equation	(dW)/(dh)=0.0018h^2	$\frac{d W}{d h} = 0.0018 h^{2}$
73627	Solve the Differential Equation	(x+1)(dy)/(dx)=2y	$(x + 1) \frac{d y}{d x} = 2 y$
73628	Solve the Differential Equation	(dy)/(dx)=5x^3y-3xy	$\frac{d y}{d x} = 5 x^{3} y - 3 x y$
73629	Solve the Differential Equation	(dy)/(dt)=(te^t)/(y square root of 1+y^2)	$\frac{d y}{d t} = \frac{t e^{t}}{y \sqrt{1 + y^{2}}}$
73630	Solve the Differential Equation	y(9x-2y)dx-x(6x-y)dy=0	$y (9 x - 2 y) d x - x (6 x - y) d y = 0$
73631	Solve the Differential Equation	xyy''''=1-x^2	$x y y'' = 1 - x^{2}$
73632	Solve the Differential Equation	y''''=e^t	$y'' = e^{t}$
73633	Solve the Differential Equation	(dy)/(dx)-(2y)/x=x^3+3x^4	$\frac{d y}{d x} - \frac{2 y}{x} = x^{3} + 3 x^{4}$
73634	Solve the Differential Equation	(dy)/(dx)+y/x=xy^2	$\frac{d y}{d x} + \frac{y}{x} = x y^{2}$
73635	Solve the Differential Equation	(dy)/(dx)+1/xy=x	$\frac{d y}{d x} + \frac{1}{x} y = x$
73636	Solve the Differential Equation	(dy)/(dx)=-4x+12x^2	$\frac{d y}{d x} = - 4 x + 12 x^{2}$
73637	Solve the Differential Equation	ydx+(xy+2x-ye^y)dy=0	$yd x + (x y + 2 x - y e^{y}) d y = 0$
73638	Solve the Differential Equation	(dy)/(dx)=(1+1/(x^2))y^6	$\frac{d y}{d x} = (1 + \frac{1}{x^{2}}) y^{6}$
73639	Solve the Differential Equation	(dy)/(dx)=1-xy	$\frac{d y}{d x} = 1 - x y$
73640	Solve the Differential Equation	(y natural log of y-e^(-xy))dx+(1/y+x natural log of y)dy=0	$(y \ln (y) - e^{- x y}) d x + (\frac{1}{y} + x \ln (y)) d y = 0$
73641	Solve the Differential Equation	(dy)/(dx)=12x^2-12x	$\frac{d y}{d x} = 12 x^{2} - 12 x$
73642	Solve the Differential Equation	(ds)/(dt)=36t(9t^2-7)^3 , s(1)=5	$\frac{d s}{d t} = 36 t {(9 t^{2} - 7)}^{3}$ , $s (1) = 5$
73643	Solve the Differential Equation	(d^2y)/(dx^2)+25y=5x^2+x	$\frac{d^{2} y}{d x^{2}} + 25 y = 5 x^{2} + x$
73644	Solve the Differential Equation	(dy)/(dx)=x/y , y(0)=-7	$\frac{d y}{d x} = \frac{x}{y}$ , $y (0) = - 7$
73645	Solve the Differential Equation	(2ax+by+g)dx+(2ey+bx+h)dy=0	$(2 a x + b y + g) d x + (2 e y + b x + h) d y = 0$
73646	Solve the Differential Equation	y''''=4x^3y	$y'' = 4 x^{3} y$
73647	Solve the Differential Equation	(dy)/(dt)+ty=y	$\frac{d y}{d t} + t y = y$
73648	Solve the Differential Equation	x(dy)/(dx)=y^2-1	$x \frac{d y}{d x} = y^{2} - 1$
73649	Solve the Differential Equation	y''''=y/(3x)	$y'' = \frac{y}{3 x}$
73650	Solve the Differential Equation	(dy)/(dx)=4x^(-3/4) , y(1)=5	$\frac{d y}{d x} = 4 x^{- \frac{3}{4}}$ , $y (1) = 5$
73651	Solve the Differential Equation	(dy)/(dx)=cos(4x)	$\frac{d y}{d x} = \cos (4 x)$
73652	Solve the Differential Equation	y''''=ay	$y'' = a y$
73653	Solve the Differential Equation	(dy)/(dx)=1-7/3x^(4/3)	$\frac{d y}{d x} = 1 - \frac{7}{3} x^{\frac{4}{3}}$
73654	Solve the Differential Equation	(dy)/(dx)=(8x^3)/(3y^2) , y(0)=2	$\frac{d y}{d x} = \frac{8 x^{3}}{3 y^{2}}$ , $y (0) = 2$
73655	Solve the Differential Equation	(ds)/(dt)=2 square root of s	$\frac{d s}{d t} = 2 \sqrt{s}$
73656	Solve the Differential Equation	(2x+y)dx+(x+6y)dy=0	$(2 x + y) d x + (x + 6 y) d y = 0$
73657	Solve the Differential Equation	(dy)/(dx)-3y=1/2e^(-3x)	$\frac{d y}{d x} - 3 y = \frac{1}{2} e^{- 3 x}$
73658	Solve the Differential Equation	2x^2(d^2y)/(dx^2)-3(dy)/(dx)+y=0	$2 x^{2} \frac{d^{2} y}{d x^{2}} - 3 \frac{d y}{d x} + y = 0$
73659	Solve the Differential Equation	y''''+1/xy=2/3x^4y^4	$y'' + \frac{1}{x} y = \frac{2}{3} x^{4} y^{4}$
73660	Solve the Differential Equation	(ds)/(dt)=12t(3t^2-1)^3 , s(1)=2	$\frac{d s}{d t} = 12 t {(3 t^{2} - 1)}^{3}$ , $s (1) = 2$
73661	Solve the Differential Equation	(dy)/(dx)=-8xy	$\frac{d y}{d x} = - 8 x y$
73662	Solve the Differential Equation	y''''+y=xe^x	$y'' + y = x e^{x}$
73663	Solve the Differential Equation	(8+x^2)y''''-2xy=0	$(8 + x^{2}) y'' - 2 x y = 0$
73664	Solve the Differential Equation	(x^2-y^2)dx+2x(yd)y=0	$(x^{2} - y^{2}) d x + 2 x yd y = 0$
73665	Solve the Differential Equation	y''''-xy=x	$y'' - x y = x$
73666	Solve the Differential Equation	(x^3+y)dx+(y^3+x)dy=0	$(x^{3} + y) d x + (y^{3} + x) d y = 0$
73667	Solve the Differential Equation	(y+ square root of x^2+y^2)dx=xdy	$(y + \sqrt{x^{2} + y^{2}}) d x = x d y$
73668	Solve the Differential Equation	(2x-3y+2)dx+(2x-3y+1)dy=0	$(2 x - 3 y + 2) d x + (2 x - 3 y + 1) d y = 0$
73669	Solve the Differential Equation	sin(theta)(dr)/(dtheta)=-1-2rcos(theta)	$\sin (θ) \frac{d r}{d θ} = - 1 - 2 r \cos (θ)$
73670	Solve the Differential Equation	(dy)/(dx)=x^8y	$\frac{d y}{d x} = x^{8} y$
73671	Solve the Differential Equation	5y(dy)/(dx)=8x^2	$5 y \frac{d y}{d x} = 8 x^{2}$
73672	Solve the Differential Equation	(dr)/(dtheta)=-pisin(pitheta) , r(0)=3	$\frac{d r}{d θ} = - π \sin (π θ)$ , $r (0) = 3$
73673	Solve the Differential Equation	(dy)/(dx)+9y=3e^(3x)	$\frac{d y}{d x} + 9 y = 3 e^{3 x}$
73674	Solve the Differential Equation	f(x)=9^(x^3)	$f (x) = 9^{x^{3}}$
73675	Solve the Differential Equation	2x(dy)/(dx)=5-2x^3	$2 x \frac{d y}{d x} = 5 - 2 x^{3}$
73676	Solve the Differential Equation	xdx+sec(x)sin(ydy)=0	$x d x + \sec (x) \sin (yd y) = 0$
73677	Solve the Differential Equation	square root of 1+y^2dx+xy natural log of xdy=0	$\sqrt{1 + y^{2}} d x + x y \ln (x d y) = 0$
73678	Solve the Differential Equation	xy''''-2y=8x^2 natural log of x	$x y'' - 2 y = 8 x^{2} \ln (x)$
73679	Solve the Differential Equation	y''''=1+0.01y^2	$y'' = 1 + 0.01 y^{2}$
73680	Solve the Differential Equation	(y+ square root of x^2+y^2)dx-xdy=0	$(y + \sqrt{x^{2} + y^{2}}) d x - x d y = 0$
73681	Solve the Differential Equation	(ds)/(dt)=12t(3t^2-1)^3 , s(1)=6	$\frac{d s}{d t} = 12 t {(3 t^{2} - 1)}^{3}$ , $s (1) = 6$
73682	Solve the Differential Equation	(dy)/(dx)=15e^(-5x)	$\frac{d y}{d x} = 15 e^{- 5 x}$
73683	Solve the Differential Equation	(dy)/(dx)+2y=3e^x	$\frac{d y}{d x} + 2 y = 3 e^{x}$
73684	Solve the Differential Equation	(dx)/(dt)+2x=4e^(2t) , x(0)=2	$\frac{d x}{d t} + 2 x = 4 e^{2 t}$ , $x (0) = 2$
73685	Solve the Differential Equation	(dy)/(dx)=36x	$\frac{d y}{d x} = 36 x$
73686	Solve the Differential Equation	yy''''+2y=1+x^2	$y y'' + 2 y = 1 + x^{2}$
73687	Solve the Differential Equation	2x(y+1)+(x^2+1)(dy)/(dx)=0	$2 x (y + 1) + (x^{2} + 1) \frac{d y}{d x} = 0$
73688	Solve the Differential Equation	(2xy^2+x/(y^2))dx+4x^2(yd)y=0	$(2 x y^{2} + \frac{x}{y^{2}}) d x + 4 x^{2} yd y = 0$
73689	Solve the Differential Equation	y''''+13y=0	$y'' + 13 y = 0$
73690	Solve the Differential Equation	x(dy)/(dx)-2y=-x	$x \frac{d y}{d x} - 2 y = - x$
73691	Solve the Differential Equation	(dy)/(dx)=x/(y^4)	$\frac{d y}{d x} = \frac{x}{y^{4}}$
73692	Solve the Differential Equation	(dy)/(dx)=1+x+xy+y	$\frac{d y}{d x} = 1 + x + x y + y$
73693	Solve the Differential Equation	(y+2x)dy+ydx=0	$(y + 2 x) d y + yd x = 0$
73694	Solve the Differential Equation	(dy)/(dx)=(9e^x)/(e^y)	$\frac{d y}{d x} = \frac{9 e^{x}}{e^{y}}$
73695	Solve the Differential Equation	(d^2y)/(dx^2)+4(dy)/(dx)+6y=2cos(2x)+5sin(2x)	$\frac{d^{2} y}{d x^{2}} + 4 \frac{d y}{d x} + 6 y = 2 \cos (2 x) + 5 \sin (2 x)$
73696	Solve the Differential Equation	x(dy)/(dx)+y=1	$x \frac{d y}{d x} + y = 1$
73697	Solve the Differential Equation	(x^2+y+y^2)dx-xdy=0	$(x^{2} + y + y^{2}) d x - x d y = 0$
73698	Solve the Differential Equation	(dy)/(dx)=(x^3-21x)/(5+4x-x^2)	$\frac{d y}{d x} = \frac{x^{3} - 21 x}{5 + 4 x - x^{2}}$
73699	Solve the Differential Equation	2(dy)/(dx)-x/y+x^3cos(y)=0	$2 \frac{d y}{d x} - \frac{x}{y} + x^{3} \cos (y) = 0$
73700	Solve the Differential Equation	(ysin(x)+xycos(x))dx+(xsin(x)+1)dy=0	$(y \sin (x) + x y \cos (x)) d x + (x \sin (x) + 1) d y = 0$