Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
71101	Solve the Differential Equation	(dy)/(dx)=y+3	$\frac{d y}{d x} = y + 3$
71102	Solve the Differential Equation	(dy)/(dx)=(x^2+1)/y	$\frac{d y}{d x} = \frac{x^{2} + 1}{y}$
71103	Solve the Differential Equation	xy''''''''-y''''=0	$x y'''' - y'' = 0$
71104	Solve the Differential Equation	x(dy)/(dx)=2y	$x \frac{d y}{d x} = 2 y$
71105	Solve the Differential Equation	(dy)/(dx)=(4y)/x	$\frac{d y}{d x} = \frac{4 y}{x}$
71106	Solve the Differential Equation	y''''=-x/y	$y'' = - \frac{x}{y}$
71107	Solve the Differential Equation	(4xy+3x^2)dx+(2y+2x^2)dy=0	$(4 x y + 3 x^{2}) d x + (2 y + 2 x^{2}) d y = 0$
71108	Solve the Differential Equation	(dy)/(dx)=ye^(-x^2) , y(4)=1	$\frac{d y}{d x} = y e^{- x^{2}}$ , $y (4) = 1$
71109	Solve the Differential Equation	(1-y)y''''=x^2	$(1 - y) y'' = x^{2}$
71110	Solve the Differential Equation	(dy)/(dx)+3x^2y=6x^2	$\frac{d y}{d x} + 3 x^{2} y = 6 x^{2}$
71111	Solve the Differential Equation	(dy)/(dt)=63t^6	$\frac{d y}{d t} = 63 t^{6}$
71112	Solve the Differential Equation	y''''+70y=0	$y'' + 70 y = 0$
71113	Solve the Differential Equation	y''''=y^2x^3	$y'' = y^{2} x^{3}$
71114	Solve the Differential Equation	f(x)=x^2	$f (x) = x^{2}$
71115	Solve the Differential Equation	y''''=x+y	$y'' = x + y$
71116	Solve the Differential Equation	(4xy+3y^2-x)dx+x(x+2y)dy=0	$(4 x y + 3 y^{2} - x) d x + x (x + 2 y) d y = 0$
71117	Solve the Differential Equation	(dy)/(dx)=ky	$\frac{d y}{d x} = k y$
71118	Solve the Differential Equation	(dy)/(dx)-e^(x+y)=0	$\frac{d y}{d x} - e^{x + y} = 0$
71119	Solve the Differential Equation	(dy)/(dx)=-4y	$\frac{d y}{d x} = - 4 y$
71120	Solve the Differential Equation	dx-e^xdy=0	$d x - e^{x} d y = 0$
71121	Solve the Differential Equation	(2x^2+y)dx+(x^2y-x)dy=0	$(2 x^{2} + y) d x + (x^{2} y - x) d y = 0$
71122	Solve the Differential Equation	y''''+y=e^(2x)	$y'' + y = e^{2 x}$
71123	Solve the Differential Equation	(d^2y)/(dx^2)=2x-5	$\frac{d^{2} y}{d x^{2}} = 2 x - 5$
71124	Solve the Differential Equation	(dy)/(dx)=x+y^2	$\frac{d y}{d x} = x + y^{2}$
71125	Solve the Differential Equation	(x^2+y^2)dx-2x(yd)y=0	$(x^{2} + y^{2}) d x - 2 x yd y = 0$
71126	Solve the Differential Equation	(dy)/(dt)=45t^4	$\frac{d y}{d t} = 45 t^{4}$
71127	Solve the Differential Equation	(dy)/(dx)=9 square root of xy	$\frac{d y}{d x} = 9 \sqrt{x y}$
71128	Solve the Differential Equation	(dy)/(dt)=49t^6	$\frac{d y}{d t} = 49 t^{6}$
71129	Solve the Differential Equation	(2xy^2-5)dx+(2x^2y+4)dy=0	$(2 x y^{2} - 5) d x + (2 x^{2} y + 4) d y = 0$
71130	Solve the Differential Equation	y''''+3y=8	$y'' + 3 y = 8$
71131	Solve the Differential Equation	(dy)/(dx)=-2xy	$\frac{d y}{d x} = - 2 x y$
71132	Solve the Differential Equation	y''''=(x^2+y^2)/(xy)	$y'' = \frac{x^{2} + y^{2}}{x y}$
71133	Solve the Differential Equation	(dy)/(dx)=y/x+2x+1	$\frac{d y}{d x} = \frac{y}{x} + 2 x + 1$
71134	Solve the Differential Equation	(dy)/(dx)=2(x-1)	$\frac{d y}{d x} = 2 (x - 1)$
71135	Solve the Differential Equation	x^2y''''+xy=1	$x^{2} y'' + x y = 1$
71136	Solve the Differential Equation	(dy)/(dx)=(2x+2xy^2)/(y+2x^2y)	$\frac{d y}{d x} = \frac{2 x + 2 x y^{2}}{y + 2 x^{2} y}$
71137	Solve the Differential Equation	(dy)/(dt)=3+5y	$\frac{d y}{d t} = 3 + 5 y$
71138	Solve the Differential Equation	y(dy)/(dx)=x^2-1	$y \frac{d y}{d x} = x^{2} - 1$
71139	Solve the Differential Equation	(dy)/(dt)=45t^8	$\frac{d y}{d t} = 45 t^{8}$
71140	Solve the Differential Equation	(dP)/(dt) = square root of Pt	$\frac{d P}{d t} = \sqrt{P t}$
71141	Solve the Differential Equation	(dP)/(dt)=kP	$\frac{d P}{d t} = k P$
71142	Solve the Differential Equation	(x+7y+1)dx+(7x-y-3)dy=0	$(x + 7 y + 1) d x + (7 x - y - 3) d y = 0$
71143	Solve the Differential Equation	(dy)/(dx)=x^3+(3y)/x	$\frac{d y}{d x} = x^{3} + \frac{3 y}{x}$
71144	Solve the Differential Equation	(dy)/(dx)=1/y	$\frac{d y}{d x} = \frac{1}{y}$
71145	Solve the Differential Equation	(dy)/(dx)=(cos(x))/(cos(x)-1)	$\frac{d y}{d x} = \frac{\cos (x)}{\cos (x) - 1}$
71146	Solve the Differential Equation	(dy)/(dx)=2x^2-5	$\frac{d y}{d x} = 2 x^{2} - 5$
71147	Solve the Differential Equation	y''''+9y=0	$y'' + 9 y = 0$
71148	Solve the Differential Equation	(dy)/(dx)=x/(y^2)	$\frac{d y}{d x} = \frac{x}{y^{2}}$
71149	Solve the Differential Equation	(dy)/(dx)=(3x^2+4x+2)/(2(y-1))	$\frac{d y}{d x} = \frac{3 x^{2} + 4 x + 2}{2 (y - 1)}$
71150	Solve the Differential Equation	x(dy)/(dx)+y=x^2y^2	$x \frac{d y}{d x} + y = x^{2} y^{2}$
71151	Solve the Differential Equation	(2x^3-xy^2-2y+3)dx-(x^2y+2x)dy=0	$(2 x^{3} - x y^{2} - 2 y + 3) d x - (x^{2} y + 2 x) d y = 0$
71152	Solve the Differential Equation	(dy)/(dx)=2/(x^2+4)	$\frac{d y}{d x} = \frac{2}{x^{2} + 4}$
71153	Solve the Differential Equation	(x-y)dx+(x+y)dy=0	$(x - y) d x + (x + y) d y = 0$
71154	Solve the Differential Equation	(x^2+y^2)dx-x(yd)y=0	$(x^{2} + y^{2}) d x - x yd y = 0$
71155	Solve the Differential Equation	(y^2-xy)dx+x^2dy=0	$(y^{2} - x y) d x + x^{2} d y = 0$
71156	Solve the Differential Equation	(x^2+y^2+x)dx+x(yd)y=0	$(x^{2} + y^{2} + x) d x + x yd y = 0$
71157	Solve the Differential Equation	(dy)/(dx)+2xy=4x	$\frac{d y}{d x} + 2 x y = 4 x$
71158	Solve the Differential Equation	x^3(dy)/(dx)+3x^2y=x	$x^{3} \frac{d y}{d x} + 3 x^{2} y = x$
71159	Solve the Differential Equation	2(8)(0.9)+2(15)(dy)/(dt)=0	$2 (8) (0.9) + 2 (15) \frac{d y}{d t} = 0$
71160	Solve the Differential Equation	(dy)/(dx)=(4x)/y	$\frac{d y}{d x} = \frac{4 x}{y}$
71161	Solve the Differential Equation	(xy)dx+(2x^2+3y^2-20)dy=0	$(x y) d x + (2 x^{2} + 3 y^{2} - 20) d y = 0$
71162	Solve the Differential Equation	(dy)/(dx)=y/x-x/y	$\frac{d y}{d x} = \frac{y}{x} - \frac{x}{y}$
71163	Solve the Differential Equation	y''''=x	$y'' = x$
71164	Solve the Differential Equation	(dy)/(dx)=3x-6	$\frac{d y}{d x} = 3 x - 6$
71165	Solve the Differential Equation	(dy)/(dx)-(3y)/x=x^3 if y(1)=4	$\frac{d y}{d x} - \frac{3 y}{x} = x^{3}$ if $y (1) = 4$
71166	Solve the Differential Equation	(2x+y)dx-(x+6y)dy=0	$(2 x + y) d x - (x + 6 y) d y = 0$
71167	Solve the Differential Equation	(x-y)(4x+y)dx+x(5x-y)dy=0	$(x - y) (4 x + y) d x + x (5 x - y) d y = 0$
71168	Solve the Differential Equation	dy=y^3cos(xdx)	$d y = y^{3} \cos (x d x)$
71169	Solve the Differential Equation	(dy)/(dx)=-15x-6x^2+4x^3	$\frac{d y}{d x} = - 15 x - 6 x^{2} + 4 x^{3}$
71170	Solve the Differential Equation	(2xy^3-4y+4x-3)dx+(3x^2y^2-4x)dy=0	$(2 x y^{3} - 4 y + 4 x - 3) d x + (3 x^{2} y^{2} - 4 x) d y = 0$
71171	Solve the Differential Equation	ydx=2(x+y)dy	$yd x = 2 (x + y) d y$
71172	Solve the Differential Equation	3x^2(yd)x+(y^4-x^3)dy=0	$3 x^{2} yd x + (y^{4} - x^{3}) d y = 0$
71173	Solve the Differential Equation	(dy)/(dx)=1/x	$\frac{d y}{d x} = \frac{1}{x}$
71174	Solve the Differential Equation	y''''+y=1	$y'' + y = 1$
71175	Solve the Differential Equation	(dx)/(dt)=1-sin(2t)	$\frac{d x}{d t} = 1 - \sin (2 t)$
71176	Solve the Differential Equation	(dy)/(dx)-2xy=x	$\frac{d y}{d x} - 2 x y = x$
71177	Solve the Differential Equation	(dy)/(dx)=(x^2)/(y(1+x^3))	$\frac{d y}{d x} = \frac{x^{2}}{y (1 + x^{3})}$
71178	Solve the Differential Equation	(1+ natural log of x+y/x)dx=(1- natural log of x)dy	$(1 + \ln (x) + \frac{y}{x}) d x = (1 - \ln (x)) d y$
71179	Solve the Differential Equation	(dy)/(dx)=(x^2)/(y^3)	$\frac{d y}{d x} = \frac{x^{2}}{y^{3}}$
71180	Solve the Differential Equation	(dy)/(dx)=-3y	$\frac{d y}{d x} = - 3 y$
71181	Solve the Differential Equation	y''''''''+y''''=0	$y'''' + y'' = 0$
71182	Solve the Differential Equation	(dy)/(dx)=-y	$\frac{d y}{d x} = - y$
71183	Solve the Differential Equation	3xy''''-2y=(x^3)/(y^2)	$3 x y'' - 2 y = \frac{x^{3}}{y^{2}}$
71184	Solve the Differential Equation	(dy)/(dx)=6x	$\frac{d y}{d x} = 6 x$
71185	Solve the Differential Equation	(dy)/(dx)=( natural log of x)/(xy)	$\frac{d y}{d x} = \frac{\ln (x)}{x y}$
71186	Solve the Differential Equation	xdx+ydy=0	$x d x + yd y = 0$
71187	Solve the Differential Equation	xy''''=y-x	$x y'' = y - x$
71188	Solve the Differential Equation	y''''+2/xy=5/(x^2)y^3	$y'' + \frac{2}{x} y = \frac{5}{x^{2}} y^{3}$
71189	Solve the Differential Equation	(xy^2-x)dx+(x^2y+y)dy=0	$(x y^{2} - x) d x + (x^{2} y + y) d y = 0$
71190	Solve the Differential Equation	(x-y)dx+(3x+y)dy=0	$(x - y) d x + (3 x + y) d y = 0$
71191	Solve the Differential Equation	(r+sin(theta)-cos(theta))dr+r(sin(theta)+cos(theta))dtheta=0	$(r + \sin (θ) - \cos (θ)) d r + r (\sin (θ) + \cos (θ)) d θ = 0$
71192	Solve the Differential Equation	(dy)/(dx)=(3x^2+2x+1)/(y+1)	$\frac{d y}{d x} = \frac{3 x^{2} + 2 x + 1}{(y + 1)}$
71193	Solve the Differential Equation	dx+x(yd)y=y^2dx+ydy	$d x + x yd y = y^{2} d x + yd y$
71194	Solve the Differential Equation	(dy)/(dx)=3xy^2	$\frac{d y}{d x} = 3 x y^{2}$
71195	Solve the Differential Equation	(dy)/(dx)-2y=e^(3x)	$\frac{d y}{d x} - 2 y = e^{3 x}$
71196	Solve the Differential Equation	y''''''''-2y''''+10y=0	$y'''' - 2 y'' + 10 y = 0$
71197	Solve the Differential Equation	xy^3dx+(y+1)e^(-x)dy=0	$x y^{3} d x + (y + 1) e^{- x} d y = 0$
71198	Solve the Differential Equation	y''''=(2x)/y	$y'' = \frac{2 x}{y}$
71199	Solve the Differential Equation	(d^2y)/(dx^2)+y=0	$\frac{d^{2} y}{d x^{2}} + y = 0$
71200	Solve the Differential Equation	e^ydx+(x+1)dy=0	$e^{y} d x + (x + 1) d y = 0$