Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
73501	Solve the Differential Equation	xy''''+2y=e^x	$x y'' + 2 y = e^{x}$
73502	Solve the Differential Equation	(x^2+y^2)dx-(2xy)dy=0	$(x^{2} + y^{2}) d x - (2 x y) d y = 0$
73503	Solve the Differential Equation	(dy)/(dx)=-(4x)/y	$\frac{d y}{d x} = - \frac{4 x}{y}$
73504	Solve the Differential Equation	y''''-xy=2xy^(1/2)	$y'' - x y = 2 x y^{\frac{1}{2}}$
73505	Solve the Differential Equation	(dt)/(dv)-3/vt=v^4	$\frac{d t}{d v} - \frac{3}{v} t = v^{4}$
73506	Solve the Differential Equation	x^2y''''-2xy''''-4y=0	$x^{2} y'' - 2 x y'' - 4 y = 0$
73507	Solve the Differential Equation	y(x^4-y^2)dx+x(x^4+y^2)dy=0	$y (x^{4} - y^{2}) d x + x (x^{4} + y^{2}) d y = 0$
73508	Solve the Differential Equation	(ds)/(dt)=36t(9t^2-7)^3 , s(1)=6	$\frac{d s}{d t} = 36 t {(9 t^{2} - 7)}^{3}$ , $s (1) = 6$
73509	Solve the Differential Equation	(dy)/(dx)=1/(x^2)+x	$\frac{d y}{d x} = \frac{1}{x^{2}} + x$
73510	Solve the Differential Equation	(ds)/(dt)=28t(7t^2-5)^3 , s(1)=2	$\frac{d s}{d t} = 28 t {(7 t^{2} - 5)}^{3}$ , $s (1) = 2$
73511	Solve the Differential Equation	(dy)/(dx)+2y=sin(x)	$\frac{d y}{d x} + 2 y = \sin (x)$
73512	Solve the Differential Equation	(x+y)dx-xdy=0	$(x + y) d x - x d y = 0$
73513	Solve the Differential Equation	(dA)/(dt)=-10A	$\frac{d A}{d t} = - 10 A$
73514	Solve the Differential Equation	(dy)/(dx)-3/xy=x^3	$\frac{d y}{d x} - \frac{3}{x} y = x^{3}$
73515	Solve the Differential Equation	(dy)/(dx)-2y-3=0	$\frac{d y}{d x} - 2 y - 3 = 0$
73516	Solve the Differential Equation	(dy)/(dx)=2y+1	$\frac{d y}{d x} = 2 y + 1$
73517	Solve the Differential Equation	f(x)=\|x-1\|	$f (x) = \| x - 1 \|$
73518	Solve the Differential Equation	(dy)/(dt)=2t	$\frac{d y}{d t} = 2 t$
73519	Solve the Differential Equation	(2y^2+3xy-2y+6x)dx+(x^2+2xy-x)dy=0	$(2 y^{2} + 3 x y - 2 y + 6 x) d x + (x^{2} + 2 x y - x) d y = 0$
73520	Solve the Differential Equation	(dy)/(dx)=(4x+y+1)^2	$\frac{d y}{d x} = {(4 x + y + 1)}^{2}$
73521	Solve the Differential Equation	f(x)=e^(2x)	$f (x) = e^{2 x}$
73522	Solve the Differential Equation	x(dy)/(dx)+y=-2x^6y^4	$x \frac{d y}{d x} + y = - 2 x^{6} y^{4}$
73523	Solve the Differential Equation	ty''''+2y=4t^2	$t y'' + 2 y = 4 t^{2}$
73524	Solve the Differential Equation	(dy)/(dx) = cube root of y	$\frac{d y}{d x} = \sqrt[3]{y}$
73525	Solve the Differential Equation	6x+1/y(dy)/(dx)=12x^2	$6 x + \frac{1}{y} \cdot \frac{d y}{d x} = 12 x^{2}$
73526	Solve the Differential Equation	ydx+(x+x^3y^2)dy=0	$yd x + (x + x^{3} y^{2}) d y = 0$
73527	Solve the Differential Equation	5(dy)/(dx)+2x=3	$5 \frac{d y}{d x} + 2 x = 3$
73528	Solve the Differential Equation	(3x^2-y)dx+(3y^2-x)dy=0	$(3 x^{2} - y) d x + (3 y^{2} - x) d y = 0$
73529	Solve the Differential Equation	(dy)/(dx)=10^(x+y)	$\frac{d y}{d x} = 10^{x + y}$
73530	Solve the Differential Equation	(dy)/(dx)=1/(2 square root of x) , y(4)=0	$\frac{d y}{d x} = \frac{1}{2 \sqrt{x}}$ , $y (4) = 0$
73531	Solve the Differential Equation	(x+y)dx-xdy=0	$(x + y) d x - x d y = 0$
73532	Solve the Differential Equation	y''''=y+1	$y'' = y + 1$
73533	Solve the Differential Equation	(y^4-2xy)dx+3x^2dy=0	$(y^{4} - 2 x y) d x + 3 x^{2} d y = 0$
73534	Solve the Differential Equation	(dy)/(dx)-5=x^2	$\frac{d y}{d x} - 5 = x^{2}$
73535	Solve the Differential Equation	y''''-y=e^xy^2	$y'' - y = e^{x} y^{2}$
73536	Solve the Differential Equation	(dy)/(dx)+(3y)/x=x	$\frac{d y}{d x} + \frac{3 y}{x} = x$
73537	Solve the Differential Equation	y''''-y=8e^x	$y'' - y = 8 e^{x}$
73538	Solve the Differential Equation	x(1+y^2)dx-y(1+x^2)dy=0	$x (1 + y^{2}) d x - y (1 + x^{2}) d y = 0$
73539	Solve the Differential Equation	(dy)/(dt)+5y=0	$\frac{d y}{d t} + 5 y = 0$
73540	Solve the Differential Equation	(dy)/(dx)=tan(x+y)	$\frac{d y}{d x} = \tan (x + y)$
73541	Solve the Differential Equation	(dy)/(dx)=x^4(y-2)	$\frac{d y}{d x} = x^{4} (y - 2)$
73542	Solve the Differential Equation	(d^2y)/(dx^2)+y=x^2+2	$\frac{d^{2} y}{d x^{2}} + y = x^{2} + 2$
73543	Solve the Differential Equation	(dy)/(dx)=(x^3-3)/(cos(y))	$\frac{d y}{d x} = \frac{x^{3} - 3}{\cos (y)}$
73544	Solve the Differential Equation	y^2dx+(xy-1)dy=0	$y^{2} d x + (x y - 1) d y = 0$
73545	Solve the Differential Equation	(dy)/(dx)=1-4/3x^(1/3)	$\frac{d y}{d x} = 1 - \frac{4}{3} x^{\frac{1}{3}}$
73546	Solve the Differential Equation	(dy)/(dx)=e^(4x)	$\frac{d y}{d x} = e^{4 x}$
73547	Solve the Differential Equation	(dy)/(dt)=4y	$\frac{d y}{d t} = 4 y$
73548	Solve the Differential Equation	(xcos((pi/4)/1)^2-pi/4)dx+1dy=0	$(x \cos^{2} (\frac{\frac{π}{4}}{1}) - \frac{π}{4}) d x + 1 d y = 0$
73549	Solve the Differential Equation	x^2y''''=7	$x^{2} y'' = 7$
73550	Solve the Differential Equation	2wt(dt)/(dw)=t^2-2w^3	$2 w t \frac{d t}{d w} = t^{2} - 2 w^{3}$
73551	Solve the Differential Equation	y''''=xe^y	$y'' = x e^{y}$
73552	Solve the Differential Equation	y''''-y=16	$y'' - y = 16$
73553	Solve the Differential Equation	(dy)/(dx)=(2x)/(y+1)	$\frac{d y}{d x} = \frac{2 x}{y + 1}$
73554	Solve the Differential Equation	f(x)=11/( square root of x)	$f (x) = \frac{11}{\sqrt{x}}$
73555	Solve the Differential Equation	(dy)/(dx)-y/x=3x^2	$\frac{d y}{d x} - \frac{y}{x} = 3 x^{2}$
73556	Solve the Differential Equation	x(dy)/(dx)+y=3	$x \frac{d y}{d x} + y = 3$
73557	Solve the Differential Equation	y''''-2xy=0	$y'' - 2 x y = 0$
73558	Solve the Differential Equation	x(dy)/(dx)+(y^2)/x=y	$x \frac{d y}{d x} + \frac{y^{2}}{x} = y$
73559	Solve the Differential Equation	xy^2y''''=x+7	$x y^{2} y'' = x + 7$
73560	Solve the Differential Equation	(dy)/(dx) = natural log of x	$\frac{d y}{d x} = \ln (x)$
73561	Solve the Differential Equation	(dx)/(dt)=(x natural log of x)/t	$\frac{d x}{d t} = \frac{x \ln (x)}{t}$
73562	Solve the Differential Equation	(dy)/(dx)+2y=x^2	$\frac{d y}{d x} + 2 y = x^{2}$
73563	Solve the Differential Equation	2y''''''''+2y''''+y=0	$2 y'''' + 2 y'' + y = 0$
73564	Solve the Differential Equation	y''''=3x-y	$y'' = 3 x - y$
73565	Solve the Differential Equation	(dy)/(dx)=(4x^2)/( square root of 4+x^3)	$\frac{d y}{d x} = \frac{4 x^{2}}{\sqrt{4 + x^{3}}}$
73566	Solve the Differential Equation	(dy)/(dx)=y^2(1+x^2)	$\frac{d y}{d x} = y^{2} (1 + x^{2})$
73567	Solve the Differential Equation	yx^4dx=(1+x^2)y^(1/2)dy	$y x^{4} d x = (1 + x^{2}) y^{\frac{1}{2}} d y$
73568	Solve the Differential Equation	y''''-2y''''-3y=x+5	$y'' - 2 y'' - 3 y = x + 5$
73569	Solve the Differential Equation	xdy-(yd)x-xy^3dx-xy^3 natural log of xdx=0	$x d y - yd x - x y^{3} d x - x y^{3} \ln (x d x) = 0$
73570	Solve the Differential Equation	(dy)/(dx)=5e^(-5x)	$\frac{d y}{d x} = 5 e^{- 5 x}$
73571	Solve the Differential Equation	(dy)/(dx)=y-7	$\frac{d y}{d x} = y - 7$
73572	Solve the Differential Equation	(dx)/(dy)=y	$\frac{d x}{d y} = y$
73573	Solve the Differential Equation	y''''''''''''-y''''''''=0	$y'''''' - y'''' = 0$
73574	Solve the Differential Equation	(1+x^2+y^2+x^2y^2)dy=y^2dx	$(1 + x^{2} + y^{2} + x^{2} y^{2}) d y = y^{2} d x$
73575	Solve the Differential Equation	2x(yd)x=(x^2-y^2)dy	$2 x yd x = (x^{2} - y^{2}) d y$
73576	Solve the Differential Equation	yy''''=8cos(x)	$y y'' = 8 \cos (x)$
73577	Solve the Differential Equation	ty''''+2y=t^2-t+1	$t y'' + 2 y = t^{2} - t + 1$
73578	Solve the Differential Equation	(dP)/(dx)=4x^3	$\frac{d P}{d x} = 4 x^{3}$
73579	Solve the Differential Equation	y''''''''-4y''''+4y=(x+1)e^(2x)	$y'''' - 4 y'' + 4 y = (x + 1) e^{2 x}$
73580	Solve the Differential Equation	x(dy)/(dx)=5y	$x \frac{d y}{d x} = 5 y$
73581	Solve the Differential Equation	(3x^2y+8xy^2)dx+(x^3+8x^2y+12y^2)dy=0	$(3 x^{2} y + 8 x y^{2}) d x + (x^{3} + 8 x^{2} y + 12 y^{2}) d y = 0$
73582	Solve the Differential Equation	2y''''''''-7y''''=-29	$2 y'''' - 7 y'' = - 29$
73583	Solve the Differential Equation	xy''''-3y=x^2	$x y'' - 3 y = x^{2}$
73584	Solve the Differential Equation	(dy)/(dx)=7/((6+x)^2) , y(0)=6	$\frac{d y}{d x} = \frac{7}{{(6 + x)}^{2}}$ , $y (0) = 6$
73585	Solve the Differential Equation	(x+3x^3sin(y))dx+(x^4cos(y))dy=0	$(x + 3 x^{3} \sin (y)) d x + (x^{4} \cos (y)) d y = 0$
73586	Solve the Differential Equation	2(d^5x)/(ds^5)-7(d^4x)/(ds^4)+12(d^3x)/(ds^3)+8(d^2x)/(ds^2)=0	$2 \frac{d^{5} x}{d s^{5}} - 7 \frac{d^{4} x}{d s^{4}} + 12 \frac{d^{3} x}{d s^{3}} + 8 \frac{d^{2} x}{d s^{2}} = 0$
73587	Solve the Differential Equation	(dy)/(dx)+1/3y=1/3(1+3x)y^4	$\frac{d y}{d x} + \frac{1}{3} y = \frac{1}{3} (1 + 3 x) y^{4}$
73588	Solve the Differential Equation	(ds)/(dt)=1/(t^2)+cos(t)	$\frac{d s}{d t} = \frac{1}{t^{2}} + \cos (t)$
73589	Solve the Differential Equation	(dy)/(dx)=(8x^2)/(9y^2)	$\frac{d y}{d x} = \frac{8 x^{2}}{9 y^{2}}$
73590	Solve the Differential Equation	(ds)/(dt)=28t(7t^2-5)^3	$\frac{d s}{d t} = 28 t {(7 t^{2} - 5)}^{3}$
73591	Solve the Differential Equation	(4xy+y^2)dx-(2x^2-2y)dy=0	$(4 x y + y^{2}) d x - (2 x^{2} - 2 y) d y = 0$
73592	Solve the Differential Equation	(dy)/(y^3)=e^(2x)dx	$\frac{d y}{y^{3}} = e^{2 x} d x$
73593	Solve the Differential Equation	(dy)/(dx)=4/(x-6) and y(7)=-2	$\frac{d y}{d x} = \frac{4}{x - 6}$ and $y (7) = - 2$
73594	Solve the Differential Equation	y''''+y=e^xy^2	$y'' + y = e^{x} y^{2}$
73595	Solve the Differential Equation	x^2y''''''''-xy''''+y=0	$x^{2} y'''' - x y'' + y = 0$
73596	Solve the Differential Equation	y''''=csc(x)+ycot(x)	$y'' = \csc (x) + y \cot (x)$
73597	Solve the Differential Equation	2y''''''''-3y''''+4y=0	$2 y'''' - 3 y'' + 4 y = 0$
73598	Solve the Differential Equation	(dy)/(dx)=(y^2+x^2)/(xy)	$\frac{d y}{d x} = \frac{y^{2} + x^{2}}{x y}$
73599	Solve the Differential Equation	y''''+y/x=0	$y'' + \frac{y}{x} = 0$
73600	Solve the Differential Equation	xy''''=7	$x y'' = 7$