Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
73201	Solve the Differential Equation	y(2x^2-xy+y^2)dx-x^2(2x-y)dy=0	$y (2 x^{2} - x y + y^{2}) d x - x^{2} (2 x - y) d y = 0$
73202	Solve the Differential Equation	(dy)/(dx)=(x^2+1)/(2-2y)	$\frac{d y}{d x} = \frac{x^{2} + 1}{2 - 2 y}$
73203	Solve the Differential Equation	y''''-2y=4	$y'' - 2 y = 4$
73204	Solve the Differential Equation	y''''+y=5	$y'' + y = 5$
73205	Solve the Differential Equation	(dy)/(dt)=sin(5t)	$\frac{d y}{d t} = \sin (5 t)$
73206	Solve the Differential Equation	square root of 2xy(dy)/(dx)=1	$\sqrt{2 x y} \frac{d y}{d x} = 1$
73207	Solve the Differential Equation	(dy)/(dx)=sin(3x)	$\frac{d y}{d x} = \sin (3 x)$
73208	Solve the Differential Equation	(ds)/(dt)=cos(t)-sin(t) , s(pi/2)=4	$\frac{d s}{d t} = \cos (t) - \sin (t)$ , $s (\frac{π}{2}) = 4$
73209	Solve the Differential Equation	(x-1)^2(yd)x+x^2(y+1)dy=0	${(x - 1)}^{2} yd x + x^{2} (y + 1) d y = 0$
73210	Solve the Differential Equation	(dr)/(ds)=0.5r	$\frac{d r}{d s} = 0.5 r$
73211	Solve the Differential Equation	y''''=(y+4x)^2	$y'' = {(y + 4 x)}^{2}$
73212	Solve the Differential Equation	(dy)/(dx)=4/(xe^y)	$\frac{d y}{d x} = \frac{4}{x e^{y}}$
73213	Solve the Differential Equation	y''''-2xy=2x	$y'' - 2 x y = 2 x$
73214	Solve the Differential Equation	(dy)/(dx)=3-y	$\frac{d y}{d x} = 3 - y$
73215	Solve the Differential Equation	(dy)/(dx)=(2x^2y+y^3)/(2x^3)	$\frac{d y}{d x} = \frac{2 x^{2} y + y^{3}}{2 x^{3}}$
73216	Solve the Differential Equation	y''''''''-y=e^x	$y'''' - y = e^{x}$
73217	Solve the Differential Equation	(dy)/(dx)=3	$\frac{d y}{d x} = 3$
73218	Solve the Differential Equation	(3x^2y^3-5x^4)dx+(y+3x^3y^2)dy=0	$(3 x^{2} y^{3} - 5 x^{4}) d x + (y + 3 x^{3} y^{2}) d y = 0$
73219	Solve the Differential Equation	(dy)/(dx)=(3x^2)/y	$\frac{d y}{d x} = \frac{3 x^{2}}{y}$
73220	Solve the Differential Equation	(dR)/(dt)=3.17-6.671/t	$\frac{d R}{d t} = 3.17 - \frac{6.671}{t}$
73221	Solve the Differential Equation	y''''=3/(2 square root of t)	$y'' = \frac{3}{2 \sqrt{t}}$
73222	Solve the Differential Equation	(dy)/(dx)=8x^3-3x^2+9x	$\frac{d y}{d x} = 8 x^{3} - 3 x^{2} + 9 x$
73223	Solve the Differential Equation	(dy)/(dx)=y^2cos(x)	$\frac{d y}{d x} = y^{2} \cos (x)$
73224	Solve the Differential Equation	(dA)/(dt)=9A	$\frac{d A}{d t} = 9 A$
73225	Solve the Differential Equation	(dy)/(dx)=(3x^2)/(5y)	$\frac{d y}{d x} = \frac{3 x^{2}}{5 y}$
73226	Solve the Differential Equation	xy^2y''''=x+8	$x y^{2} y'' = x + 8$
73227	Solve the Differential Equation	(dy)/(dx)=-(4y^2)/(x^3)	$\frac{d y}{d x} = - \frac{4 y^{2}}{x^{3}}$
73228	Solve the Differential Equation	(du)/(dt)=(2t+sec(t)^2)/(2u)	$\frac{d u}{d t} = \frac{2 t + \sec^{2} (t)}{2 u}$
73229	Solve the Differential Equation	xy''''+2y=0	$x y'' + 2 y = 0$
73230	Solve the Differential Equation	(dy)/(dx)=cos(x)cos(y)^2 , y(0)=pi/4	$\frac{d y}{d x} = \cos (x) \cos^{2} (y)$ , $y (0) = \frac{π}{4}$
73231	Solve the Differential Equation	(dL)/(dt)=kL^2 natural log of t	$\frac{dL}{d t} = {kL}^{2} \ln (t)$
73232	Solve the Differential Equation	(3x^2-2xy+3y^2)dx=4x(yd)y	$(3 x^{2} - 2 x y + 3 y^{2}) d x = 4 x yd y$
73233	Solve the Differential Equation	(dy)/(dx)+(3y)/x=(e^x)/(x^3)	$\frac{d y}{d x} + \frac{3 y}{x} = \frac{e^{x}}{x^{3}}$
73234	Solve the Differential Equation	(y^2-y)(dy)/(dx)=x	$(y^{2} - y) \frac{d y}{d x} = x$
73235	Solve the Differential Equation	7y(dy)/(dx)=2x^2	$7 y \frac{d y}{d x} = 2 x^{2}$
73236	Solve the Differential Equation	y^3y''''+x^3=0	$y^{3} y'' + x^{3} = 0$
73237	Solve the Differential Equation	(dy)/(dx)+2xy=6x	$\frac{d y}{d x} + 2 x y = 6 x$
73238	Solve the Differential Equation	(1-x)y''''''''-4xy''''+5y=cos(x)	$(1 - x) y'''' - 4 x y'' + 5 y = \cos (x)$
73239	Solve the Differential Equation	(ds)/(dt)=8sin(t+pi/12)^2 , s(0)=6	$\frac{d s}{d t} = 8 \sin^{2} (t + \frac{π}{12})$ , $s (0) = 6$
73240	Solve the Differential Equation	x^2(dy)/(dx)-y^2=2xy	$x^{2} \frac{d y}{d x} - y^{2} = 2 x y$
73241	Solve the Differential Equation	dx+(x/y-sin(y))dy=0	$d x + (\frac{x}{y} - \sin (y)) d y = 0$
73242	Solve the Differential Equation	(dy)/(dx)=xe^x	$\frac{d y}{d x} = x e^{x}$
73243	Solve the Differential Equation	y''''+y/(x+1)=0	$y'' + \frac{y}{x + 1} = 0$
73244	Solve the Differential Equation	(dy)/(dx)+xe^y=0	$\frac{d y}{d x} + x e^{y} = 0$
73245	Solve the Differential Equation	(dy)/(dx)=10-x , y(0)=-1	$\frac{d y}{d x} = 10 - x$ , $y (0) = - 1$
73246	Solve the Differential Equation	(dy)/(dx)=y-20	$\frac{d y}{d x} = y - 20$
73247	Solve the Differential Equation	(dy)/(dx)=cos(2x)	$\frac{d y}{d x} = \cos (2 x)$
73248	Solve the Differential Equation	dy=18x^2dx	$d y = 18 x^{2} d x$
73249	Solve the Differential Equation	(dy)/(dx)+y=xy^2	$\frac{d y}{d x} + y = x y^{2}$
73250	Solve the Differential Equation	(du)/(dt)=(2t+sec(t)^2)/(2u) , u(0)=-5	$\frac{d u}{d t} = \frac{2 t + \sec^{2} (t)}{2 u}$ , $u (0) = - 5$
73251	Solve the Differential Equation	(dy)/(dx) = square root of y	$\frac{d y}{d x} = \sqrt{y}$
73252	Solve the Differential Equation	(dtheta)/(dr)=e^(2theta)sin(r)	$\frac{d θ}{d r} = e^{2 θ} \sin (r)$
73253	Solve the Differential Equation	(dy)/(dx)=(1+y^2)e^x	$\frac{d y}{d x} = (1 + y^{2}) e^{x}$
73254	Solve the Differential Equation	e^y(dy)/(dx)=4x	$e^{y} \frac{d y}{d x} = 4 x$
73255	Solve the Differential Equation	(ds)/(dt)=5 square root of s	$\frac{d s}{d t} = 5 \sqrt{s}$
73256	Solve the Differential Equation	xdy=(3-2y)dx	$x d y = (3 - 2 y) d x$
73257	Solve the Differential Equation	3(dy)/(dtheta)=(e^ysin(theta)^2)/(ysec(theta))	$3 \frac{d y}{d θ} = \frac{e^{y} \sin^{2} (θ)}{y \sec (θ)}$
73258	Solve the Differential Equation	f(x) = natural log of 2x^3-5x	$f (x) = \ln (2 x^{3} - 5 x)$
73259	Solve the Differential Equation	2x^3(dy)/(dx)=y(y^2+3x^2)	$2 x^{3} \frac{d y}{d x} = y (y^{2} + 3 x^{2})$
73260	Solve the Differential Equation	(dy)/(dx)-2xy=3x	$\frac{d y}{d x} - 2 x y = 3 x$
73261	Solve the Differential Equation	y''''''''''''-2y''''''''-y''''+2y=0	$y'''''' - 2 y'''' - y'' + 2 y = 0$
73262	Solve the Differential Equation	(dy)/(dx)=8x^3-3x^2+5x	$\frac{d y}{d x} = 8 x^{3} - 3 x^{2} + 5 x$
73263	Solve the Differential Equation	(1+y^2)dx=xdy	$(1 + y^{2}) d x = x d y$
73264	Solve the Differential Equation	(x^2+y^2)dx+4x(yd)y=0	$(x^{2} + y^{2}) d x + 4 x yd y = 0$
73265	Solve the Differential Equation	(x-2)^2y''''+5(x-2)y''''+8y=0	${(x - 2)}^{2} y'' + 5 (x - 2) y'' + 8 y = 0$
73266	Solve the Differential Equation	(dy)/(dx)=(x^2+2y^2)/(xy)	$\frac{d y}{d x} = \frac{x^{2} + 2 y^{2}}{x y}$
73267	Solve the Differential Equation	2xy(dy)/(dx)=y^2-x^2	$2 x y \frac{d y}{d x} = y^{2} - x^{2}$
73268	Solve the Differential Equation	(dy)/(dx)=(cos(x)+sin(x))/(2y)	$\frac{d y}{d x} = \frac{\cos (x) + \sin (x)}{2 y}$
73269	Solve the Differential Equation	y''''+y=y^3	$y'' + y = y^{3}$
73270	Solve the Differential Equation	y^2dx+(3xy-1)dy=0	$y^{2} d x + (3 x y - 1) d y = 0$
73271	Solve the Differential Equation	y''''+(1/(3x))y=x^2	$y'' + (\frac{1}{3 x}) y = x^{2}$
73272	Solve the Differential Equation	(dy)/(dx)=(24x)/(e^y)	$\frac{d y}{d x} = \frac{24 x}{e^{y}}$
73273	Solve the Differential Equation	x(x+y)dy=(x^2+y^2)dx	$x (x + y) d y = (x^{2} + y^{2}) d x$
73274	Solve the Differential Equation	(9x-4y+4)dx-(2x-y+1)dy=0	$(9 x - 4 y + 4) d x - (2 x - y + 1) d y = 0$
73275	Solve the Differential Equation	(dy)/(dx)=(y^2-x^2)/(xy)	$\frac{d y}{d x} = \frac{y^{2} - x^{2}}{x y}$
73276	Solve the Differential Equation	x^2dy+y(x+y)dx=0	$x^{2} d y + y (x + y) d x = 0$
73277	Solve the Differential Equation	xy''''=y(x/(x+1))	$x y'' = y (\frac{x}{x + 1})$
73278	Solve the Differential Equation	(4x+y)dx+(x-2y)dy=0	$(4 x + y) d x + (x - 2 y) d y = 0$
73279	Solve the Differential Equation	f(x)=1/3e^(x^3)	$f (x) = \frac{1}{3} e^{x^{3}}$
73280	Solve the Differential Equation	y''''=y+5	$y'' = y + 5$
73281	Solve the Differential Equation	y''''=(2x)/(y+x^2y)	$y'' = \frac{2 x}{y + x^{2} y}$
73282	Solve the Differential Equation	(ds)/(dt)=8sin(t-pi/12)^2 , s(0)=6	$\frac{d s}{d t} = 8 \sin^{2} (t - \frac{π}{12})$ , $s (0) = 6$
73283	Solve the Differential Equation	y''''-2/(x^2)y=0	$y'' - \frac{2}{x^{2}} y = 0$
73284	Solve the Differential Equation	(dy)/(dx)=x^2+x^2y^2	$\frac{d y}{d x} = x^{2} + x^{2} y^{2}$
73285	Solve the Differential Equation	(dy)/(dx)=2+3y	$\frac{d y}{d x} = 2 + 3 y$
73286	Solve the Differential Equation	2x(yd)x+(x^2-1)dy=0	$2 x yd x + (x^{2} - 1) d y = 0$
73287	Solve the Differential Equation	3t^3dx=x(x^2+2t^2)dt	$3 t^{3} d x = x (x^{2} + 2 t^{2}) d t$
73288	Solve the Differential Equation	(2xy-sin(x))dx+(x^2-cos(y))dy=0	$(2 x y - \sin (x)) d x + (x^{2} - \cos (y)) d y = 0$
73289	Solve the Differential Equation	(ds)/(dt)+s/t=cos(t)+(sin(t))/t	$\frac{d s}{d t} + \frac{s}{t} = \cos (t) + \frac{\sin (t)}{t}$
73290	Solve the Differential Equation	y^2dx-(xy+2)dx=0	$y^{2} d x - (x y + 2) d x = 0$
73291	Solve the Differential Equation	x^2(d^2y)/(dx^2)=2	$x^{2} \frac{d^{2} y}{d x^{2}} = 2$
73292	Solve the Differential Equation	square root of 1-4x^2(dy)/(dx)=x	$\sqrt{1 - 4 x^{2}} \frac{d y}{d x} = x$
73293	Solve the Differential Equation	(x^2+9)y''''=xy	$(x^{2} + 9) y'' = x y$
73294	Solve the Differential Equation	(dy)/(dx)=12e^(-3x)	$\frac{d y}{d x} = 12 e^{- 3 x}$
73295	Solve the Differential Equation	(dy)/(dx)=2y+x^2+5	$\frac{d y}{d x} = 2 y + x^{2} + 5$
73296	Solve the Differential Equation	(2x+3y)dx+(y-x)dy=0	$(2 x + 3 y) d x + (y - x) d y = 0$
73297	Solve the Differential Equation	y''''-2y=y^2	$y'' - 2 y = y^{2}$
73298	Solve the Differential Equation	(dy)/(dx)=30x	$\frac{d y}{d x} = 30 x$
73299	Solve the Differential Equation	(dy)/(dx)=5	$\frac{d y}{d x} = 5$
73300	Solve the Differential Equation	(dr)/(dtheta)=-picos(pitheta) , r(0)=2	$\frac{d r}{d θ} = - π \cos (π θ)$ , $r (0) = 2$