Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70901	Solve the Differential Equation	(dy)/(dx)=xe^y	$\frac{d y}{d x} = x e^{y}$
70902	Solve the Differential Equation	y''''+3x^2y=x^2	$y'' + 3 x^{2} y = x^{2}$
70903	Solve the Differential Equation	(dy)/(dx)+2y=0	$\frac{d y}{d x} + 2 y = 0$
70904	Solve the Differential Equation	(dy)/(dx)=3/x	$\frac{d y}{d x} = \frac{3}{x}$
70905	Solve the Differential Equation	y''''''''+9y=0	$y'''' + 9 y = 0$
70906	Solve the Differential Equation	(dz)/(dt)+2e^(t+z)=0	$\frac{d z}{d t} + 2 e^{t + z} = 0$
70907	Solve the Differential Equation	y''''''''+4y=0	$y'''' + 4 y = 0$
70908	Solve the Differential Equation	sin(x)sin(ydx)+cos(x)cos(ydy)=0	$\sin (x) \sin (yd x) + \cos (x) \cos (yd y) = 0$
70909	Solve the Differential Equation	(dy)/(dx)=e^(-y)	$\frac{d y}{d x} = e^{- y}$
70910	Solve the Differential Equation	(2xy^2-3)dx+(2x^2y+4)dy=0	$(2 x y^{2} - 3) d x + (2 x^{2} y + 4) d y = 0$
70911	Solve the Differential Equation	y''''-2xy=x	$y'' - 2 x y = x$
70912	Solve the Differential Equation	solve the differential equation of (dy)/(dx)=2/(x^2+4)	solve the differential equation of $\frac{d y}{d x} = \frac{2}{x^{2} + 4}$
70913	Solve the Differential Equation	y''''=2xy	$y'' = 2 x y$
70914	Solve the Differential Equation	(dz)/(dx)=(z+4)/(2z-1)+1	$\frac{d z}{d x} = \frac{z + 4}{2 z - 1} + 1$
70915	Solve the Differential Equation	2(2x^2+y^2)dx-x(yd)y=0	$2 (2 x^{2} + y^{2}) d x - x yd y = 0$
70916	Solve the Differential Equation	(dz)/(dt)+6e^(t+z)=0	$\frac{d z}{d t} + 6 e^{t + z} = 0$
70917	Solve the Differential Equation	(dy)/(dx)=cos(y)^2	$\frac{d y}{d x} = \cos^{2} (y)$
70918	Solve the Differential Equation	(dy)/(dx)-3y=6	$\frac{d y}{d x} - 3 y = 6$
70919	Solve the Differential Equation	(x^2+y^2)dx-x(yd)y=0	$(x^{2} + y^{2}) d x - x yd y = 0$
70920	Solve the Differential Equation	(dy)/(dx)=cos(x+y)	$\frac{d y}{d x} = \cos (x + y)$
70921	Solve the Differential Equation	(dy)/(dx)=(x^2-1)/(y^2)	$\frac{d y}{d x} = \frac{x^{2} - 1}{y^{2}}$
70922	Solve the Differential Equation	y''''=e^(-3x)sin(6x)	$y'' = e^{- 3 x} \sin (6 x)$
70923	Solve the Differential Equation	(1-x)(dy)/(dx)=y^2	$(1 - x) \frac{d y}{d x} = y^{2}$
70924	Solve the Differential Equation	(1+y^2)dx+(1+x^2)dy=0	$(1 + y^{2}) d x + (1 + x^{2}) d y = 0$
70925	Solve the Differential Equation	(du)/(dv)=(-2v)/u	$\frac{d u}{d v} = \frac{- 2 v}{u}$
70926	Solve the Differential Equation	(dz)/(dt)+5e^(t+z)=0	$\frac{d z}{d t} + 5 e^{t + z} = 0$
70927	Solve the Differential Equation	y''''+y=y^2	$y'' + y = y^{2}$
70928	Solve the Differential Equation	(dy)/(dx)=7x square root of y	$\frac{d y}{d x} = 7 x \sqrt{y}$
70929	Solve the Differential Equation	(dz)/(dt)+4e^(t+z)=0	$\frac{d z}{d t} + 4 e^{t + z} = 0$
70930	Solve the Differential Equation	y''''-3y=6	$y'' - 3 y = 6$
70931	Solve the Differential Equation	(dy)/(dx)=y/x+x/y	$\frac{d y}{d x} = \frac{y}{x} + \frac{x}{y}$
70932	Solve the Differential Equation	3x(dy)/(dx)=x^2	$3 x \frac{d y}{d x} = x^{2}$
70933	Solve the Differential Equation	x(dy)/(dx)=sec(y)	$x \frac{d y}{d x} = \sec (y)$
70934	Solve the Differential Equation	(dy)/(dx)=3x^2	$\frac{d y}{d x} = 3 x^{2}$
70935	Solve the Differential Equation	(dy)/(dx)=7y^2x^3	$\frac{d y}{d x} = 7 y^{2} x^{3}$
70936	Solve the Differential Equation	(d^2y)/(dx^2)=1/(x^2)	$\frac{d^{2} y}{d x^{2}} = \frac{1}{x^{2}}$
70937	Solve the Differential Equation	(x-2y)dx+(2x+y)dy=0	$(x - 2 y) d x + (2 x + y) d y = 0$
70938	Solve the Differential Equation	xcos(ydx)^2+tan(ydy)=0	$x \cos^{2} (yd x) + \tan (yd y) = 0$
70939	Solve the Differential Equation	x(yd)x-(x^2+3y^2)dy=0	$x yd x - (x^{2} + 3 y^{2}) d y = 0$
70940	Solve the Differential Equation	(dy)/(dx)=xy+y	$\frac{d y}{d x} = x y + y$
70941	Solve the Differential Equation	(du)/(dt)=e^(u+2t)	$\frac{d u}{d t} = e^{u + 2 t}$
70942	Solve the Differential Equation	(dp)/(dt)=p-p^2	$\frac{d p}{d t} = p - p^{2}$
70943	Solve the Differential Equation	(dy)/(dx)=(4x+xy^2)/(y-x^2y)	$\frac{d y}{d x} = \frac{4 x + x y^{2}}{y - x^{2} y}$
70944	Solve the Differential Equation	y''''=x-y	$y'' = x - y$
70945	Solve the Differential Equation	(x+y)dx+xdy=0	$(x + y) d x + x d y = 0$
70946	Solve the Differential Equation	(dy)/(dx)=2x-y	$\frac{d y}{d x} = 2 x - y$
70947	Solve the Differential Equation	y''''=(y+x)/x	$y'' = \frac{y + x}{x}$
70948	Solve the Differential Equation	y''''=x/y	$y'' = \frac{x}{y}$
70949	Solve the Differential Equation	y''''+ytan(x)=0	$y'' + y \tan (x) = 0$
70950	Solve the Differential Equation	xy''''-2y=x^3cos(4x)	$x y'' - 2 y = x^{3} \cos (4 x)$
70951	Solve the Differential Equation	(dy)/(dx)+2x=3x^2	$\frac{d y}{d x} + 2 x = 3 x^{2}$
70952	Solve the Differential Equation	y''''+ycos(x)=cos(x)sin(x)	$y'' + y \cos (x) = \cos (x) \sin (x)$
70953	Solve the Differential Equation	(x^2+6y^2)dx-4x(yd)y=0	$(x^{2} + 6 y^{2}) d x - 4 x yd y = 0$
70954	Solve the Differential Equation	(dy)/(dx)=-y/x	$\frac{d y}{d x} = - \frac{y}{x}$
70955	Solve the Differential Equation	(dy)/(dx)=(x^2+y^2)/(xy)	$\frac{d y}{d x} = \frac{x^{2} + y^{2}}{x y}$
70956	Solve the Differential Equation	(dz)/(dt)+7e^(t+z)=0	$\frac{d z}{d t} + 7 e^{t + z} = 0$
70957	Solve the Differential Equation	xy''''+y=xy^3	$x y'' + y = x y^{3}$
70958	Solve the Differential Equation	x(dy)/(dx)+y=x^3	$x \frac{d y}{d x} + y = x^{3}$
70959	Solve the Differential Equation	(dy)/(dx)=y+2	$\frac{d y}{d x} = y + 2$
70960	Solve the Differential Equation	y''''=1/xy+1	$y'' = \frac{1}{x} y + 1$
70961	Solve the Differential Equation	x(dy)/(dx)+4y=x^3-x	$x \frac{d y}{d x} + 4 y = x^{3} - x$
70962	Solve the Differential Equation	(2xy-3x^2)dx+(x^2+y)dy=0	$(2 x y - 3 x^{2}) d x + (x^{2} + y) d y = 0$
70963	Solve the Differential Equation	(dy)/(dt)=15t^2	$\frac{d y}{d t} = 15 t^{2}$
70964	Solve the Differential Equation	(dy)/(dx)=x/(y+1)	$\frac{d y}{d x} = \frac{x}{y + 1}$
70965	Solve the Differential Equation	e^x(dy)/(dx)=2x	$e^{x} \frac{d y}{d x} = 2 x$
70966	Solve the Differential Equation	(dy)/(dx)+2y=x	$\frac{d y}{d x} + 2 y = x$
70967	Solve the Differential Equation	(dy)/(dx)+4y=y(e^x+4)	$\frac{d y}{d x} + 4 y = y (e^{x} + 4)$
70968	Solve the Differential Equation	y''''''''-4y=0	$y'''' - 4 y = 0$
70969	Solve the Differential Equation	(dz)/(dt)+3e^(t+z)=0	$\frac{d z}{d t} + 3 e^{t + z} = 0$
70970	Solve the Differential Equation	(dy)/(dx)=(x^3)/(y^2)	$\frac{d y}{d x} = \frac{x^{3}}{y^{2}}$
70971	Solve the Differential Equation	(dy)/(dx)=2xy^2	$\frac{d y}{d x} = 2 x y^{2}$
70972	Solve the Differential Equation	(x^2-y^2)dx+(x^2-2xy)dy=0	$(x^{2} - y^{2}) d x + (x^{2} - 2 x y) d y = 0$
70973	Solve the Differential Equation	y''''+2y=0	$y'' + 2 y = 0$
70974	Solve the Differential Equation	y''''-5y=0	$y'' - 5 y = 0$
70975	Solve the Differential Equation	(dy)/(dx)=(x^2+xy+y^2)/(x^2)	$\frac{d y}{d x} = \frac{x^{2} + x y + y^{2}}{x^{2}}$
70976	Solve the Differential Equation	(dy)/(dx)=(x+y)/x	$\frac{d y}{d x} = \frac{x + y}{x}$
70977	Solve the Differential Equation	(dy)/(dt)=35t^4	$\frac{d y}{d t} = 35 t^{4}$
70978	Solve the Differential Equation	(dy)/(dx)=12x^3e^(-2y)	$\frac{d y}{d x} = 12 x^{3} e^{- 2 y}$
70979	Solve the Differential Equation	y^2dy+x^3dx=0	$y^{2} d y + x^{3} d x = 0$
70980	Solve the Differential Equation	ye^(2x)dx=(4+e^(2x))dy	$y e^{2 x} d x = (4 + e^{2 x}) d y$
70981	Solve the Differential Equation	(dy)/(dx)-y=xy^5	$\frac{d y}{d x} - y = x y^{5}$
70982	Solve the Differential Equation	y''''=(3x^2+4x-4)/(2y-4)	$y'' = \frac{3 x^{2} + 4 x - 4}{2 y - 4}$
70983	Solve the Differential Equation	y''''=y^2	$y'' = y^{2}$
70984	Solve the Differential Equation	(dy)/(dx)=4x-5	$\frac{d y}{d x} = 4 x - 5$
70985	Solve the Differential Equation	(dy)/(dx)+70y=0	$\frac{d y}{d x} + 70 y = 0$
70986	Solve the Differential Equation	(dy)/(dx)=y(xy^3-1)	$\frac{d y}{d x} = y (x y^{3} - 1)$
70987	Solve the Differential Equation	(dy)/(dx)=7y	$\frac{d y}{d x} = 7 y$
70988	Solve the Differential Equation	(dy)/(dx)=2x-1	$\frac{d y}{d x} = 2 x - 1$
70989	Solve the Differential Equation	(dy)/(dx)=xy-4x	$\frac{d y}{d x} = x y - 4 x$
70990	Solve the Differential Equation	(y^2-2xy+6x)dx-(x^2-2xy+2)dy=0	$(y^{2} - 2 x y + 6 x) d x - (x^{2} - 2 x y + 2) d y = 0$
70991	Solve the Differential Equation	(x^3+y^3)dx+3xy^2dy=0	$(x^{3} + y^{3}) d x + 3 x y^{2} d y = 0$
70992	Solve the Differential Equation	(dy)/(dx)=4xy	$\frac{d y}{d x} = 4 x y$
70993	Solve the Differential Equation	y''''=y/x	$y'' = \frac{y}{x}$
70994	Solve the Differential Equation	(dy)/(dx)=(x^2)/y if y(0)=3	$\frac{d y}{d x} = \frac{x^{2}}{y}$ if $y (0) = 3$
70995	Solve the Differential Equation	(dx)/(dt)+x^2=x	$\frac{d x}{d t} + x^{2} = x$
70996	Solve the Differential Equation	xdx+(y-2x)dy=0	$x d x + (y - 2 x) d y = 0$
70997	Solve the Differential Equation	(dy)/(dx)=x/y+y/x	$\frac{d y}{d x} = \frac{x}{y} + \frac{y}{x}$
70998	Solve the Differential Equation	(dy)/(dx)=xy^3	$\frac{d y}{d x} = x y^{3}$
70999	Solve the Differential Equation	y^3dx-x^3dy=0	$y^{3} d x - x^{3} d y = 0$
71000	Solve the Differential Equation	xy''''+y+xy^2=0	$x y'' + y + x y^{2} = 0$