Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72001	Solve the Differential Equation	(xy+y^2)dx+(x+2y-1)dy=0	$(x y + y^{2}) d x + (x + 2 y - 1) d y = 0$
72002	Solve the Differential Equation	2x(yd)x+x^2dy=0	$2 x yd x + x^{2} d y = 0$
72003	Solve the Differential Equation	y(dy)/(dx)=x^2-x	$y \frac{d y}{d x} = x^{2} - x$
72004	Solve the Differential Equation	(dy)/(dx)=(xy-3y+x-3)/(xy+2y-x-2)	$\frac{d y}{d x} = \frac{x y - 3 y + x - 3}{x y + 2 y - x - 2}$
72005	Solve the Differential Equation	(dy)/(dx)=1/(x+y^2)	$\frac{d y}{d x} = \frac{1}{x + y^{2}}$
72006	Solve the Differential Equation	x(dy)/(dx)=y+ square root of x^2+y^2	$x \frac{d y}{d x} = y + \sqrt{x^{2} + y^{2}}$
72007	Solve the Differential Equation	(dy)/(dx)=1/(2+x) , y(0)=3	$\frac{d y}{d x} = \frac{1}{2 + x}$ , $y (0) = 3$
72008	Solve the Differential Equation	(dv)/(dp)=-V/p	$\frac{d v}{d p} = - \frac{V}{p}$
72009	Solve the Differential Equation	3x(y^2+1)dx+y(x^2+2)dy=0	$3 x (y^{2} + 1) d x + y (x^{2} + 2) d y = 0$
72010	Solve the Differential Equation	(dy)/(dx)-2xy=2	$\frac{d y}{d x} - 2 x y = 2$
72011	Solve the Differential Equation	(dy)/(dx)=x+1 , y(2)=3	$\frac{d y}{d x} = x + 1$ , $y (2) = 3$
72012	Solve the Differential Equation	(dy)/(dx)=2xe^(-y)	$\frac{d y}{d x} = 2 x e^{- y}$
72013	Solve the Differential Equation	3x(xy-2)dx+(x^3+2y)dy=0	$3 x (x y - 2) d x + (x^{3} + 2 y) d y = 0$
72014	Solve the Differential Equation	5y(dy)/(dx)=6x^2	$5 y \frac{d y}{d x} = 6 x^{2}$
72015	Solve the Differential Equation	(dy)/(dx)-y=e^x	$\frac{d y}{d x} - y = e^{x}$
72016	Solve the Differential Equation	x^2y^2dy=(y+1)dx	$x^{2} y^{2} d y = (y + 1) d x$
72017	Solve the Differential Equation	(2xy+y-e^(-x))dx+xdy=0	$(2 x y + y - e^{- x}) d x + x d y = 0$
72018	Solve the Differential Equation	(dy)/(dx)=(cos(3x))/(sin(2y))	$\frac{d y}{d x} = \frac{\cos (3 x)}{\sin (2 y)}$
72019	Solve the Differential Equation	3y''''''''-y''''=0	$3 y'''' - y'' = 0$
72020	Solve the Differential Equation	(y+1)dx-xdy=0	$(y + 1) d x - x d y = 0$
72021	Solve the Differential Equation	6xy''''+y=18x	$6 x y'' + y = 18 x$
72022	Solve the Differential Equation	y''''=1	$y'' = 1$
72023	Solve the Differential Equation	(dy)/(dx)=(1+y^2)/(1+x^2)	$\frac{d y}{d x} = \frac{1 + y^{2}}{1 + x^{2}}$
72024	Solve the Differential Equation	(dy)/(dx)=y-y^2	$\frac{d y}{d x} = y - y^{2}$
72025	Solve the Differential Equation	(y+2)dx+(x+y^2)dy=0	$(y + 2) d x + (x + y^{2}) d y = 0$
72026	Solve the Differential Equation	(dy)/(dx)=-10x+6x^2	$\frac{d y}{d x} = - 10 x + 6 x^{2}$
72027	Solve the Differential Equation	y^2dx+(3xy+y^2-1)dy=0	$y^{2} d x + (3 x y + y^{2} - 1) d y = 0$
72028	Solve the Differential Equation	(dr)/(dq)=178-q-1.5q^2	$\frac{d r}{d q} = 178 - q - 1.5 q^{2}$
72029	Solve the Differential Equation	xy''''=3y^2-y^2	$x y'' = 3 y^{2} - y^{2}$
72030	Solve the Differential Equation	(dy)/x=(dx)/y	$\frac{d y}{x} = \frac{d x}{y}$
72031	Solve the Differential Equation	(dy)/(dx)=x*(6-y)	$\frac{d y}{d x} = x \cdot (6 - y)$
72032	Solve the Differential Equation	(dy)/(dx)=-1/3x^3	$\frac{d y}{d x} = - \frac{1}{3} x^{3}$
72033	Solve the Differential Equation	(x^4+y^4)dx-xy^3dy=0	$(x^{4} + y^{4}) d x - x y^{3} d y = 0$
72034	Solve the Differential Equation	(dp)/(dt)+20p-240=0	$\frac{d p}{d t} + 20 p - 240 = 0$
72035	Solve the Differential Equation	xy''''=y^2+y	$x y'' = y^{2} + y$
72036	Solve the Differential Equation	(dy)/(dx)=y^4	$\frac{d y}{d x} = y^{4}$
72037	Solve the Differential Equation	-9/15(dtheta)/(dt)=1/15(18)	$- \frac{9}{15} \cdot \frac{d θ}{d t} = \frac{1}{15} (18)$
72038	Solve the Differential Equation	(dy)/(dx)-y/x=x^2	$\frac{d y}{d x} - \frac{y}{x} = x^{2}$
72039	Solve the Differential Equation	y''''=e^(x+2y)	$y'' = e^{x + 2 y}$
72040	Solve the Differential Equation	(dy)/(dx)=1+e^(2x)	$\frac{d y}{d x} = 1 + e^{2 x}$
72041	Solve the Differential Equation	(dy)/(dx)=(x^2+5)/(2y-1)	$\frac{d y}{d x} = \frac{(x^{2} + 5)}{2 y - 1}$
72042	Solve the Differential Equation	x(d^3y)/(dx^3)-((dy)/(dx))^4+y=0	$x \frac{d^{3} y}{d x^{3}} - {(\frac{d y}{d x})}^{4} + y = 0$
72043	Solve the Differential Equation	(x+1)(dy)/(dx)+(x+2)y=2xe^(-x)	$(x + 1) \frac{d y}{d x} + (x + 2) y = 2 x e^{- x}$
72044	Solve the Differential Equation	(1-x^2)(dy)/(dx)=2y	$(1 - x^{2}) \frac{d y}{d x} = 2 y$
72045	Solve the Differential Equation	y''''+5xe^y=0	$y'' + 5 x e^{y} = 0$
72046	Solve the Differential Equation	(dy)/(dx)=x^2-2y	$\frac{d y}{d x} = x^{2} - 2 y$
72047	Solve the Differential Equation	(xy+1)dx+(xy-1)dy=0	$(x y + 1) d x + (x y - 1) d y = 0$
72048	Solve the Differential Equation	y''''+2y=y^2	$y'' + 2 y = y^{2}$
72049	Solve the Differential Equation	y''''=x+3	$y'' = x + 3$
72050	Solve the Differential Equation	(dy)/(dx)=6x^5sec(y)	$\frac{d y}{d x} = 6 x^{5} \sec (y)$
72051	Solve the Differential Equation	y''''=-x	$y'' = - x$
72052	Solve the Differential Equation	(x-4)y^4dx-x^3(y^2-3)dy=0	$(x - 4) y^{4} d x - x^{3} (y^{2} - 3) d y = 0$
72053	Solve the Differential Equation	y''''=3x^2+5	$y'' = 3 x^{2} + 5$
72054	Solve the Differential Equation	4(dy)/(dx)-12xy-3x=0	$4 \frac{d y}{d x} - 12 x y - 3 x = 0$
72055	Solve the Differential Equation	y''''=(x+y)^2	$y'' = {(x + y)}^{2}$
72056	Solve the Differential Equation	y''''+16y=0	$y'' + 16 y = 0$
72057	Solve the Differential Equation	( square root of 1+x^2)/(2+y)(dy)/(dx)=-2x	$\frac{\sqrt{1 + x^{2}}}{2 + y} \cdot \frac{d y}{d x} = - 2 x$
72058	Solve the Differential Equation	t(dy)/(dt)-2y=t^5sin(2t)-t^3+4t^4	$t \frac{d y}{d t} - 2 y = t^{5} \sin (2 t) - t^{3} + 4 t^{4}$
72059	Solve the Differential Equation	(dy)/(dx)=(y(x-y))/(x^2)	$\frac{d y}{d x} = \frac{y (x - y)}{x^{2}}$
72060	Solve the Differential Equation	y''''=1/2x square root of 1-16y^2	$y'' = \frac{1}{2} x \sqrt{1 - 16 y^{2}}$
72061	Solve the Differential Equation	2 square root of xy(dy)/(dx)=1	$2 \sqrt{x y} \frac{d y}{d x} = 1$
72062	Solve the Differential Equation	(3x-2y+1)dx+(3x-2y+3)dy=0	$(3 x - 2 y + 1) d x + (3 x - 2 y + 3) d y = 0$
72063	Solve the Differential Equation	(dy)/(dx)=cos(X)	$\frac{d y}{d x} = \cos (X)$
72064	Solve the Differential Equation	(dy)/(dx)=8x	$\frac{d y}{d x} = 8 x$
72065	Solve the Differential Equation	4(dy)/(dx)-20xy-5x=0	$4 \frac{d y}{d x} - 20 x y - 5 x = 0$
72066	Solve the Differential Equation	(dy)/(dx)=-8/(x-7) , y(8)=-9	$\frac{d y}{d x} = - \frac{8}{x - 7}$ , $y (8) = - 9$
72067	Solve the Differential Equation	(dy)/(dx)=1/(6x-42)	$\frac{d y}{d x} = \frac{1}{6 x - 42}$
72068	Solve the Differential Equation	(1-x)y''''=e^y	$(1 - x) y'' = e^{y}$
72069	Solve the Differential Equation	x(dy)/(dx)=x+y	$x \frac{d y}{d x} = x + y$
72070	Solve the Differential Equation	(dy)/(dx)+y/x=x	$\frac{d y}{d x} + \frac{y}{x} = x$
72071	Solve the Differential Equation	(dy)/(dx)+(3y)/x=6x^2	$\frac{d y}{d x} + \frac{3 y}{x} = 6 x^{2}$
72072	Solve the Differential Equation	(dy)/(dx)=5x-6	$\frac{d y}{d x} = 5 x - 6$
72073	Solve the Differential Equation	(dy)/(dx)=4x^3	$\frac{d y}{d x} = 4 x^{3}$
72074	Solve the Differential Equation	y''''+120y=0	$y'' + 120 y = 0$
72075	Solve the Differential Equation	(dy)/(dx)=(cos(x))e^(y+sin(x))	$\frac{d y}{d x} = (\cos (x)) e^{y + \sin (x)}$
72076	Solve the Differential Equation	xy''''+y = square root of x	$x y'' + y = \sqrt{x}$
72077	Solve the Differential Equation	(dy)/(dx)=(6x)/y	$\frac{d y}{d x} = \frac{6 x}{y}$
72078	Solve the Differential Equation	y''''=0	$y'' = 0$
72079	Solve the Differential Equation	(dy)/(dx)=1-x	$\frac{d y}{d x} = 1 - x$
72080	Solve the Differential Equation	(dy)/(dx)=1-y^2	$\frac{d y}{d x} = 1 - y^{2}$
72081	Solve the Differential Equation	y''''-7y=14x	$y'' - 7 y = 14 x$
72082	Solve the Differential Equation	y(x^2+y^2)dx-x(x^2-y^2)dy=0	$y (x^{2} + y^{2}) d x - x (x^{2} - y^{2}) d y = 0$
72083	Solve the Differential Equation	y^2+10*(dy)/(dx)=0	$y^{2} + 10 \cdot \frac{d y}{d x} = 0$
72084	Solve the Differential Equation	(dy)/(dx)=-4xy	$\frac{d y}{d x} = - 4 x y$
72085	Solve the Differential Equation	(dy)/(dx)=14/x	$\frac{d y}{d x} = \frac{14}{x}$
72086	Solve the Differential Equation	x(dy)/(dx) = square root of 1-y^2	$x \frac{d y}{d x} = \sqrt{1 - y^{2}}$
72087	Solve the Differential Equation	(y-x-10)(dy)/(dx)=y-x	$(y - x - 10) \frac{d y}{d x} = y - x$
72088	Solve the Differential Equation	(dy)/(dx)=e^(5x-5y)	$\frac{d y}{d x} = e^{5 x - 5 y}$
72089	Solve the Differential Equation	x^2((dy)/(dx))-2xy=x^4+3	$x^{2} (\frac{d y}{d x}) - 2 x y = x^{4} + 3$
72090	Solve the Differential Equation	y''''''''''''-6y''''''''+12y''''-8y=0	$y'''''' - 6 y'''' + 12 y'' - 8 y = 0$
72091	Solve the Differential Equation	(dy)/(dx)=-12y	$\frac{d y}{d x} = - 12 y$
72092	Solve the Differential Equation	2x^5y''''=y(3x^4+y^2)	$2 x^{5} y'' = y (3 x^{4} + y^{2})$
72093	Solve the Differential Equation	(dy)/(dx)=14x	$\frac{d y}{d x} = 14 x$
72094	Solve the Differential Equation	(y^2+1)dx+x^2y^2dy=0	$(y^{2} + 1) d x + x^{2} y^{2} d y = 0$
72095	Solve the Differential Equation	(dy)/(dx)-5y=3	$\frac{d y}{d x} - 5 y = 3$
72096	Solve the Differential Equation	z^2(dy)/(dz)+y^2=zy	$z^{2} \frac{d y}{d z} + y^{2} = z y$
72097	Solve the Differential Equation	(dy)/(dx)=cos(3x)	$\frac{d y}{d x} = \cos (3 x)$
72098	Solve the Differential Equation	(dy)/(dx)=(4e^x)/(e^y)	$\frac{d y}{d x} = \frac{4 e^{x}}{e^{y}}$
72099	Solve the Differential Equation	x((dy)/(dx))=4y	$x (\frac{d y}{d x}) = 4 y$
72100	Solve the Differential Equation	xy(dy)/(dx)=2x^2+3y^2	$x y \frac{d y}{d x} = 2 x^{2} + 3 y^{2}$