Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72601	Solve the Differential Equation	y''''=6y	$y'' = 6 y$
72602	Solve the Differential Equation	(dy)/(dt)=k*y	$\frac{d y}{d t} = k \cdot y$
72603	Solve the Differential Equation	e^ydx+(2y+xe^y)dy=0	$e^{y} d x + (2 y + x e^{y}) d y = 0$
72604	Solve the Differential Equation	(dy)/(dx)=2x(1+x^2-y)	$\frac{d y}{d x} = 2 x (1 + x^{2} - y)$
72605	Solve the Differential Equation	x^4(dy)/(dx)+2x^3y=1	$x^{4} \frac{d y}{d x} + 2 x^{3} y = 1$
72606	Solve the Differential Equation	y''''+1/xy=3x	$y'' + \frac{1}{x} y = 3 x$
72607	Solve the Differential Equation	(dy)/(dx)=-4x^5e^y	$\frac{d y}{d x} = - 4 x^{5} e^{y}$
72608	Solve the Differential Equation	(dy)/(dx)-y/x=2x^2	$\frac{d y}{d x} - \frac{y}{x} = 2 x^{2}$
72609	Solve the Differential Equation	(2x-y)dx+(4x+y-3)dy=0	$(2 x - y) d x + (4 x + y - 3) d y = 0$
72610	Solve the Differential Equation	4x^2y''''''''+y=0	$4 x^{2} y'''' + y = 0$
72611	Solve the Differential Equation	y''''''''''''+4y''''=0	$y'''''' + 4 y'' = 0$
72612	Solve the Differential Equation	xy''''-3y=6	$x y'' - 3 y = 6$
72613	Solve the Differential Equation	(dy)/(dx)-(2y)/(x+1)=(x+1)^3	$\frac{d y}{d x} - \frac{2 y}{x + 1} = {(x + 1)}^{3}$
72614	Solve the Differential Equation	(dy)/(dx)=e^(0.25x)	$\frac{d y}{d x} = e^{0.25 x}$
72615	Solve the Differential Equation	(dy)/(dx)=e^(y+x)	$\frac{d y}{d x} = e^{y + x}$
72616	Solve the Differential Equation	(ds)/(dt)=36t(9t^2-7)^3	$\frac{d s}{d t} = 36 t {(9 t^{2} - 7)}^{3}$
72617	Solve the Differential Equation	(dy)/(dx)=x^3y^2	$\frac{d y}{d x} = x^{3} y^{2}$
72618	Solve the Differential Equation	(dy)/(dx)=(1+x)(1+y)	$\frac{d y}{d x} = (1 + x) (1 + y)$
72619	Solve the Differential Equation	y''''=7x-y	$y'' = 7 x - y$
72620	Solve the Differential Equation	(dy)/(dx)+3y=6	$\frac{d y}{d x} + 3 y = 6$
72621	Solve the Differential Equation	(2x+5)dx-dy=0	$(2 x + 5) d x - d y = 0$
72622	Solve the Differential Equation	(3x^2+6xy^2)dx+(6x^2y+4y^3)dy=0	$(3 x^{2} + 6 x y^{2}) d x + (6 x^{2} y + 4 y^{3}) d y = 0$
72623	Solve the Differential Equation	16(d^4y)/(dx^4)+24(d^2y)/(dx^2)+9y=0	$16 \frac{d^{4} y}{d x^{4}} + 24 \frac{d^{2} y}{d x^{2}} + 9 y = 0$
72624	Solve the Differential Equation	(dy)/(dx)=x/(2y)	$\frac{d y}{d x} = \frac{x}{2 y}$
72625	Solve the Differential Equation	(ds)/(dt)=12t(3t^2-1)^3 , s(1)=13	$\frac{d s}{d t} = 12 t {(3 t^{2} - 1)}^{3}$ , $s (1) = 13$
72626	Solve the Differential Equation	(3xy+3y-4)dx+(x+1)^2dy=0	$(3 x y + 3 y - 4) d x + {(x + 1)}^{2} d y = 0$
72627	Solve the Differential Equation	y''''''''-25y=0	$y'''' - 25 y = 0$
72628	Solve the Differential Equation	(dy)/(dx)=-0.1y	$\frac{d y}{d x} = - 0.1 y$
72629	Solve the Differential Equation	(du)/(dt)=2+2u+t+tu	$\frac{d u}{d t} = 2 + 2 u + t + t u$
72630	Solve the Differential Equation	(9+2xsin(y))dx-x^2cos(ydy)=0	$(9 + 2 x \sin (y)) d x - x^{2} \cos (yd y) = 0$
72631	Solve the Differential Equation	xy''''=y+xe^(y/x)	$x y'' = y + x e^{\frac{y}{x}}$
72632	Solve the Differential Equation	(dy)/(dx)=-10x^3e^y	$\frac{d y}{d x} = - 10 x^{3} e^{y}$
72633	Solve the Differential Equation	xe^(-t)(dx)/(dt)=t given the initial condition that x(0)=1	$x e^{- t} \frac{d x}{d t} = t$ given the initial condition that $x (0) = 1$
72634	Solve the Differential Equation	2x^2-y(dy)/(dx)=0	$2 x^{2} - y \frac{d y}{d x} = 0$
72635	Solve the Differential Equation	(dy)/(dx)+2y=x^2+2x	$\frac{d y}{d x} + 2 y = x^{2} + 2 x$
72636	Solve the Differential Equation	(d^2y)/(dx^2)+4(dy)/(dx)+4y=2x+6	$\frac{d^{2} y}{d x^{2}} + 4 \frac{d y}{d x} + 4 y = 2 x + 6$
72637	Solve the Differential Equation	f(x)=3x^(5/6)+7x^(2/3)	$f (x) = 3 x^{\frac{5}{6}} + 7 x^{\frac{2}{3}}$
72638	Solve the Differential Equation	(x+3y)dx-xdy=0	$(x + 3 y) d x - x d y = 0$
72639	Solve the Differential Equation	e^x(dy)/(dx)+2e^xy=1	$e^{x} \frac{d y}{d x} + 2 e^{x} y = 1$
72640	Solve the Differential Equation	(dy)/(dx)+y=y^-2	$\frac{d y}{d x} + y = y^{- 2}$
72641	Solve the Differential Equation	y''''''''''''-4y''''''''+y''''+6y=0	$y'''''' - 4 y'''' + y'' + 6 y = 0$
72642	Solve the Differential Equation	(x-2y)dx-(2x+y)dy=0	$(x - 2 y) d x - (2 x + y) d y = 0$
72643	Solve the Differential Equation	xy''''''''+y''''=x	$x y'''' + y'' = x$
72644	Solve the Differential Equation	(dy)/(dx)=(9x)/y	$\frac{d y}{d x} = \frac{9 x}{y}$
72645	Solve the Differential Equation	(dy)/(dx)=(12e^x)/(e^y)	$\frac{d y}{d x} = \frac{12 e^{x}}{e^{y}}$
72646	Solve the Differential Equation	y=y''''(x+1)	$y = y'' (x + 1)$
72647	Solve the Differential Equation	x(yd)x+(2x^2+3y^2-20)dy=0	$x yd x + (2 x^{2} + 3 y^{2} - 20) d y = 0$
72648	Solve the Differential Equation	(dy)/(dx)=e^(3x)	$\frac{d y}{d x} = e^{3 x}$
72649	Solve the Differential Equation	(dy)/(dx)=(22x)/(e^y)	$\frac{d y}{d x} = \frac{22 x}{e^{y}}$
72650	Solve the Differential Equation	ydx+(2 square root of xy-x)dy=0	$yd x + (2 \sqrt{x y} - x) d y = 0$
72651	Solve the Differential Equation	(x^2-1)(dy)/(dx)+2y=(x+1)^2	$(x^{2} - 1) \frac{d y}{d x} + 2 y = {(x + 1)}^{2}$
72652	Solve the Differential Equation	(dy)/(dx)+2xy=(2x+1)e^x	$\frac{d y}{d x} + 2 x y = (2 x + 1) e^{x}$
72653	Solve the Differential Equation	(dy)/(dx)=-6x+3x^2	$\frac{d y}{d x} = - 6 x + 3 x^{2}$
72654	Solve the Differential Equation	(dv)/(dt)=-Av	$\frac{d v}{d t} = - A v$
72655	Solve the Differential Equation	1/xdx+dy=0	$\frac{1}{x} d x + d y = 0$
72656	Solve the Differential Equation	(dy)/(dx)=1/(2y)	$\frac{d y}{d x} = \frac{1}{2 y}$
72657	Solve the Differential Equation	2y(dy)/(dx)=-4x	$2 y \frac{d y}{d x} = - 4 x$
72658	Solve the Differential Equation	(dy)/(dx)=e^(-x^2) , y(3)=5	$\frac{d y}{d x} = e^{- x^{2}}$ , $y (3) = 5$
72659	Solve the Differential Equation	(dy)/(dx)=1/3(1+3x)y^4-1/3y	$\frac{d y}{d x} = \frac{1}{3} (1 + 3 x) y^{4} - \frac{1}{3} y$
72660	Solve the Differential Equation	(dy)/(dx)=sin(5x+pi) , y(0)=6	$\frac{d y}{d x} = \sin (5 x + π)$ , $y (0) = 6$
72661	Solve the Differential Equation	y''''=5x-y	$y'' = 5 x - y$
72662	Solve the Differential Equation	(dy)/(dx)=(18x)/(e^y)	$\frac{d y}{d x} = \frac{18 x}{e^{y}}$
72663	Solve the Differential Equation	ydx-xdy=0	$yd x - x d y = 0$
72664	Solve the Differential Equation	y''''=x+y+1	$y'' = x + y + 1$
72665	Solve the Differential Equation	(dy)/(dx)=(sec(y)^2)/(1+x^2)	$\frac{d y}{d x} = \frac{\sec^{2} (y)}{1 + x^{2}}$
72666	Solve the Differential Equation	(dy)/(dx)+5y=50	$\frac{d y}{d x} + 5 y = 50$
72667	Solve the Differential Equation	(dy)/(dx)=(xy)/(x^2+y^2)	$\frac{d y}{d x} = \frac{x y}{x^{2} + y^{2}}$
72668	Solve the Differential Equation	(dy)/(dx)=(x-2)e^(-2y)	$\frac{d y}{d x} = (x - 2) e^{- 2 y}$
72669	Solve the Differential Equation	(dy)/(dx)=(4x^3)/(cos(y))	$\frac{d y}{d x} = \frac{4 x^{3}}{\cos (y)}$
72670	Solve the Differential Equation	ydx+(2x+1-xy)dy=0	$yd x + (2 x + 1 - x y) d y = 0$
72671	Solve the Differential Equation	y^2dx+(xy+y^2-1)dy=0	$y^{2} d x + (x y + y^{2} - 1) d y = 0$
72672	Solve the Differential Equation	(5x-2y)dx-x(yd)y=0	$(5 x - 2 y) d x - x yd y = 0$
72673	Solve the Differential Equation	(dy)/(dx)=(x+1)/(y+2)	$\frac{d y}{d x} = \frac{x + 1}{y + 2}$
72674	Solve the Differential Equation	(dy)/(dx)+p(x)y=0	$\frac{d y}{d x} + p (x) y = 0$
72675	Solve the Differential Equation	(dy)/(dx)+4xy=2x	$\frac{d y}{d x} + 4 x y = 2 x$
72676	Solve the Differential Equation	y''''''''+2y''''-y=0	$y'''' + 2 y'' - y = 0$
72677	Solve the Differential Equation	x^2y''''+3xy=6x-y''''	$x^{2} y'' + 3 x y = 6 x - y''$
72678	Solve the Differential Equation	(dy)/(dx)=(4 square root of y natural log of x)/x	$\frac{d y}{d x} = \frac{4 \sqrt{y} \ln (x)}{x}$
72679	Solve the Differential Equation	y''''=(x^2y-y)/(y+1)	$y'' = \frac{x^{2} y - y}{y + 1}$
72680	Solve the Differential Equation	(dy)/(dx)+(2y)/x=6x^3	$\frac{d y}{d x} + \frac{2 y}{x} = 6 x^{3}$
72681	Solve the Differential Equation	(1+ natural log of x)dx+(1+ natural log of y)dy=0	$(1 + \ln (x)) d x + (1 + \ln (y)) d y = 0$
72682	Solve the Differential Equation	f(x)=(7x-2)^2	$f (x) = {(7 x - 2)}^{2}$
72683	Solve the Differential Equation	(dy)/(dx)=4e^(x+y)	$\frac{d y}{d x} = 4 e^{x + y}$
72684	Solve the Differential Equation	(dy)/(dx)=x/(4y)	$\frac{d y}{d x} = \frac{x}{4 y}$
72685	Solve the Differential Equation	(x+y)^2(dy)/(dx)=a^2	${(x + y)}^{2} \frac{d y}{d x} = a^{2}$
72686	Solve the Differential Equation	y(x^2+y^2-1)dx+x(x^2+y^2+1)dy=0	$y (x^{2} + y^{2} - 1) d x + x (x^{2} + y^{2} + 1) d y = 0$
72687	Solve the Differential Equation	(ds)/(dt)=cos(t)-sin(t) , s(pi/2)=6	$\frac{d s}{d t} = \cos (t) - \sin (t)$ , $s (\frac{π}{2}) = 6$
72688	Solve the Differential Equation	(dy)/(dx)=e^(-x)	$\frac{d y}{d x} = e^{- x}$
72689	Solve the Differential Equation	y''''=4 square root of y	$y'' = 4 \sqrt{y}$
72690	Solve the Differential Equation	(dy)/(dx)=x/y , y(0)=-5	$\frac{d y}{d x} = \frac{x}{y}$ , $y (0) = - 5$
72691	Solve the Differential Equation	(dy)/(dx)=(x^2+5)/(2y-1)	$\frac{d y}{d x} = \frac{x^{2} + 5}{2 y - 1}$
72692	Solve the Differential Equation	xy(dy)/(dx)=1+y^2	$x y \frac{d y}{d x} = 1 + y^{2}$
72693	Solve the Differential Equation	y''''=1+x+y^2+xy^2	$y'' = 1 + x + y^{2} + x y^{2}$
72694	Solve the Differential Equation	xy''''+y=x^3	$x y'' + y = x^{3}$
72695	Solve the Differential Equation	(dy)/(dx)=(ux-x)/(ux-x)	$\frac{d y}{d x} = \frac{u x - x}{u x - x}$
72696	Solve the Differential Equation	(dy)/(dx)=(xy^2)/4	$\frac{d y}{d x} = \frac{x y^{2}}{4}$
72697	Solve the Differential Equation	(dy)/(dx)=(y-4)/(5x)	$\frac{d y}{d x} = \frac{y - 4}{5 x}$
72698	Solve the Differential Equation	(dy)/(dx)=-3sec(x-7)^2 , y(7)=7	$\frac{d y}{d x} = - 3 \sec^{2} (x - 7)$ , $y (7) = 7$
72699	Solve the Differential Equation	xcos(y)^2dx+tan(y)dy=0	$x \cos^{2} (y) d x + \tan (y) d y = 0$
72700	Solve the Differential Equation	xy''''-2y=0	$x y'' - 2 y = 0$