Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72901	Solve the Differential Equation	(1+x^4)dy+x(1+4y^2)dx=0	$(1 + x^{4}) d y + x (1 + 4 y^{2}) d x = 0$
72902	Solve the Differential Equation	(x+1)(dy)/(dx)+y=x^2-1	$(x + 1) \frac{d y}{d x} + y = x^{2} - 1$
72903	Solve the Differential Equation	ydx=(e^y+2xy-2x)dy	$yd x = (e^{y} + 2 x y - 2 x) d y$
72904	Solve the Differential Equation	(dy)/(dx)=-1-y^4	$\frac{d y}{d x} = - 1 - y^{4}$
72905	Solve the Differential Equation	(dy)/(dx)+((2x+1)/x)y=e^(-2x)	$\frac{d y}{d x} + (\frac{2 x + 1}{x}) y = e^{- 2 x}$
72906	Solve the Differential Equation	xy^2y''''=x^3+y^3	$x y^{2} y'' = x^{3} + y^{3}$
72907	Solve the Differential Equation	y''''+2y=e^(-x)	$y'' + 2 y = e^{- x}$
72908	Solve the Differential Equation	ydx+(x+2/y)dy=0	$yd x + (x + \frac{2}{y}) d y = 0$
72909	Solve the Differential Equation	(x^2+y^2)dx-x^2dy=0	$(x^{2} + y^{2}) d x - x^{2} d y = 0$
72910	Solve the Differential Equation	(dy)/(dx)=(x-1)/y	$\frac{d y}{d x} = \frac{x - 1}{y}$
72911	Solve the Differential Equation	(dr)/(dtheta)=-picos(pitheta) , r(1)=2	$\frac{d r}{d θ} = - π \cos (π θ)$ , $r (1) = 2$
72912	Solve the Differential Equation	(2y+3x)dx+xdy=0	$(2 y + 3 x) d x + x d y = 0$
72913	Solve the Differential Equation	(2x+3y-2)dx+(3x-4y+1)dy=0	$(2 x + 3 y - 2) d x + (3 x - 4 y + 1) d y = 0$
72914	Solve the Differential Equation	(dy)/(dx)+(2y)/x=4x	$\frac{d y}{d x} + \frac{2 y}{x} = 4 x$
72915	Solve the Differential Equation	y''''''''=tan(x)	$y'''' = \tan (x)$
72916	Solve the Differential Equation	y''''-y=4	$y'' - y = 4$
72917	Solve the Differential Equation	xd(yd)x+2y=x^2	$x d yd x + 2 y = x^{2}$
72918	Solve the Differential Equation	-(yd)x+(x+ square root of xy)dy=0	$- yd x + (x + \sqrt{x y}) d y = 0$
72919	Solve the Differential Equation	y''''+y=e^(-x)	$y'' + y = e^{- x}$
72920	Solve the Differential Equation	(dy)/(dx)=y-3	$\frac{d y}{d x} = y - 3$
72921	Solve the Differential Equation	(ds)/(dt)=20t(5t^2-3)^3 , s(1)=1	$\frac{d s}{d t} = 20 t {(5 t^{2} - 3)}^{3}$ , $s (1) = 1$
72922	Solve the Differential Equation	2y''''+1=4y+cos(x)^2+sin(x)^2-16x	$2 y'' + 1 = 4 y + \cos^{2} (x) + \sin^{2} (x) - 16 x$
72923	Solve the Differential Equation	(dy)/(dx)=2/x+5csc(x)^2+x	$\frac{d y}{d x} = \frac{2}{x} + 5 \csc^{2} (x) + x$
72924	Solve the Differential Equation	y''''+y/x=y^2	$y'' + \frac{y}{x} = y^{2}$
72925	Solve the Differential Equation	(y+x)dy=(x-y)dx	$(y + x) d y = (x - y) d x$
72926	Solve the Differential Equation	(dy)/(dx)=(3-y)cos(x)	$\frac{d y}{d x} = (3 - y) \cos (x)$
72927	Verify the Differential Equation Solution	(dy)/(dx)=(x^2)/y if y(0)=3	$\frac{d y}{d x} = \frac{x^{2}}{y}$ if $y (0) = 3$
72928	Solve the Differential Equation	(2xy+3)dx+(x^2-1)dy=0	$(2 x y + 3) d x + (x^{2} - 1) d y = 0$
72929	Solve the Differential Equation	y natural log of x(dx)/(dy)=((y-1)/x)^2	$y \ln (x) \frac{d x}{d y} = {(\frac{y - 1}{x})}^{2}$
72930	Solve the Differential Equation	(dy)/(dx)=(x^2+1)/(y^2-1)	$\frac{d y}{d x} = \frac{x^{2} + 1}{y^{2} - 1}$
72931	Solve the Differential Equation	(x^3+xy^2-y)dx+(y^3+x^2y-x)dy=0	$(x^{3} + x y^{2} - y) d x + (y^{3} + x^{2} y - x) d y = 0$
72932	Solve the Differential Equation	(x+2y^2)dx+x(yd)y=0	$(x + 2 y^{2}) d x + x yd y = 0$
72933	Solve the Differential Equation	(d^2y)/(dx^2)=6	$\frac{d^{2} y}{d x^{2}} = 6$
72934	Solve the Differential Equation	(1+e^x)yy''''=e^x	$(1 + e^{x}) y y'' = e^{x}$
72935	Solve the Differential Equation	(4x^2-y^2)dx-x(yd)y=0	$(4 x^{2} - y^{2}) d x - x yd y = 0$
72936	Solve the Differential Equation	y''''=x^3(1-y)	$y'' = x^{3} (1 - y)$
72937	Solve the Differential Equation	y''''-36y=0	$y'' - 36 y = 0$
72938	Solve the Differential Equation	x(dy)/(dx)+1=x+y	$x \frac{d y}{d x} + 1 = x + y$
72939	Solve the Differential Equation	(dy)/(dx)=y^2e^(-x)	$\frac{d y}{d x} = y^{2} e^{- x}$
72940	Solve the Differential Equation	(dy)/y=(dx)/(x-1)	$\frac{d y}{y} = \frac{d x}{x - 1}$
72941	Solve the Differential Equation	(dy)/(dx)=5y+y^2	$\frac{d y}{d x} = 5 y + y^{2}$
72942	Solve the Differential Equation	x^2(dy)/(dx)+3xy=x^3-x^2	$x^{2} \frac{d y}{d x} + 3 x y = x^{3} - x^{2}$
72943	Solve the Differential Equation	(dy)/(dx)=(8e^x)/(e^y)	$\frac{d y}{d x} = \frac{8 e^{x}}{e^{y}}$
72944	Solve the Differential Equation	y''''''''+6y''''+9y=2e^(-3x)	$y'''' + 6 y'' + 9 y = 2 e^{- 3 x}$
72945	Solve the Differential Equation	(dr)/(ds)=0.95r	$\frac{d r}{d s} = 0.95 r$
72946	Solve the Differential Equation	(dy)/(dx)=(-y)/x	$\frac{d y}{d x} = \frac{- y}{x}$
72947	Solve the Differential Equation	x(dy)/(dx)=x-y	$x \frac{d y}{d x} = x - y$
72948	Solve the Differential Equation	(dP)/(dt)=P(1-P)	$\frac{d P}{d t} = P (1 - P)$
72949	Solve the Differential Equation	(dy)/(dx)=(1+ square root of x)/(1+ square root of y)	$\frac{d y}{d x} = \frac{1 + \sqrt{x}}{1 + \sqrt{y}}$
72950	Solve the Differential Equation	(dy)/(dx)=4e^(-2x)	$\frac{d y}{d x} = 4 e^{- 2 x}$
72951	Solve the Differential Equation	y''''-y=4e^x	$y'' - y = 4 e^{x}$
72952	Solve the Differential Equation	(dy)/(dx)=y-17	$\frac{d y}{d x} = y - 17$
72953	Solve the Differential Equation	(dy)/(dx)=2y-4x	$\frac{d y}{d x} = 2 y - 4 x$
72954	Solve the Differential Equation	(ds)/(dt)=1/(t^2)+sin(t)	$\frac{d s}{d t} = \frac{1}{t^{2}} + \sin (t)$
72955	Solve the Differential Equation	(dy)/(dx)+y/x=sin(x)	$\frac{d y}{d x} + \frac{y}{x} = \sin (x)$
72956	Solve the Differential Equation	(1+x^2)y''''-2xy=0	$(1 + x^{2}) y'' - 2 x y = 0$
72957	Solve the Differential Equation	square root of 1-5x^2y''''=x	$\sqrt{1 - 5 x^{2}} y'' = x$
72958	Solve the Differential Equation	(dy)/(dx)=2x square root of y	$\frac{d y}{d x} = 2 x \sqrt{y}$
72959	Solve the Differential Equation	(dy)/(dx)=(cos(y)^2)/(sin(x)^2)	$\frac{d y}{d x} = \frac{\cos^{2} (y)}{\sin^{2} (x)}$
72960	Solve the Differential Equation	2x(dx)/(dt)+2y(dy)/(dt)=0	$2 x \frac{d x}{d t} + 2 y \frac{d y}{d t} = 0$
72961	Solve the Differential Equation	y''''''''-5y''''+6=0	$y'''' - 5 y'' + 6 = 0$
72962	Solve the Differential Equation	(dy)/(dx)=-(3x)/y	$\frac{d y}{d x} = - \frac{3 x}{y}$
72963	Solve the Differential Equation	(dy)/y=(dx)/x	$\frac{d y}{y} = \frac{d x}{x}$
72964	Solve the Differential Equation	(dy)/(dx)=4x^3-6x^2+3x	$\frac{d y}{d x} = 4 x^{3} - 6 x^{2} + 3 x$
72965	Solve the Differential Equation	square root of 1-3x^2y''''=x	$\sqrt{1 - 3 x^{2}} y'' = x$
72966	Solve the Differential Equation	(dy)/(dx)=(y-x+1)/(y-x+5)	$\frac{d y}{d x} = \frac{y - x + 1}{y - x + 5}$
72967	Solve the Differential Equation	(dy)/y=-(dx)/x	$\frac{d y}{y} = - \frac{d x}{x}$
72968	Solve the Differential Equation	y''''''''''''-2y''''''''+y''''=0	$y'''''' - 2 y'''' + y'' = 0$
72969	Solve the Differential Equation	(dy)/(dt)-20t^4e^(-y)=0	$\frac{d y}{d t} - 20 t^{4} e^{- y} = 0$
72970	Solve the Differential Equation	(dy)/(dx)+2y=1	$\frac{d y}{d x} + 2 y = 1$
72971	Solve the Differential Equation	x(dy)/(dx)+y=y^2	$x \frac{d y}{d x} + y = y^{2}$
72972	Solve the Differential Equation	(ds)/(dt)=8sin(t+pi/12)^2 , s(0)=4	$\frac{d s}{d t} = 8 \sin^{2} (t + \frac{π}{12})$ , $s (0) = 4$
72973	Solve the Differential Equation	(2x+y)dx-xdy=0	$(2 x + y) d x - x d y = 0$
72974	Solve the Differential Equation	(dy)/(dx)=4x^3-9x^2+3x	$\frac{d y}{d x} = 4 x^{3} - 9 x^{2} + 3 x$
72975	Solve the Differential Equation	(dy)/y=(-dx)/x	$\frac{d y}{y} = \frac{- d x}{x}$
72976	Solve the Differential Equation	-x(dy)/(dx)+y=0	$- x \frac{d y}{d x} + y = 0$
72977	Solve the Differential Equation	(dy)/(dx)-15x^2=20	$\frac{d y}{d x} - 15 x^{2} = 20$
72978	Solve the Differential Equation	(dy)/(dx)+xy=x/y	$\frac{d y}{d x} + x y = \frac{x}{y}$
72979	Solve the Differential Equation	(xcos(y/x)^2-y)dx+xdy=0	$(x \cos^{2} (\frac{y}{x}) - y) d x + x d y = 0$
72980	Solve the Differential Equation	(dy)/(dt)=0.4y^(1/2)	$\frac{d y}{d t} = 0.4 y^{\frac{1}{2}}$
72981	Solve the Differential Equation	(4y+2t-5)dt+(6y+4t-1)dy=0	$(4 y + 2 t - 5) d t + (6 y + 4 t - 1) d y = 0$
72982	Solve the Differential Equation	(2x)/ydx-(x^2)/(y^2)dy=0	$\frac{2 x}{y} d x - \frac{x^{2}}{y^{2}} d y = 0$
72983	Solve the Differential Equation	(dy)/(dx)=8x^3-9x^2+7x	$\frac{d y}{d x} = 8 x^{3} - 9 x^{2} + 7 x$
72984	Solve the Differential Equation	(dy)/(dx)=x^2-y	$\frac{d y}{d x} = x^{2} - y$
72985	Solve the Differential Equation	(dr)/(dtheta)=pisin(pitheta) , r(1)=3	$\frac{d r}{d θ} = π \sin (π θ)$ , $r (1) = 3$
72986	Solve the Differential Equation	(dy)/(dx)=3x^(-3/4) , y(1)=8	$\frac{d y}{d x} = 3 x^{- \frac{3}{4}}$ , $y (1) = 8$
72987	Solve the Differential Equation	(dy)/y+(dx)/(x^2-4x)=0	$\frac{d y}{y} + \frac{d x}{x^{2} - 4 x} = 0$
72988	Solve the Differential Equation	(dy)/(dx)=(2y)/(2x+1)	$\frac{d y}{d x} = \frac{2 y}{2 x + 1}$
72989	Solve the Differential Equation	(dy)/(dx)=e^(2x+3y) y(0)=0	$\frac{d y}{d x} = e^{2 x + 3 y}$ $y (0) = 0$
72990	Solve the Differential Equation	y''''=y-2	$y'' = y - 2$
72991	Solve the Differential Equation	(du)/(dt)=(2t+sec(t)^2)/(2u) , u(0)=-1	$\frac{d u}{d t} = \frac{2 t + \sec^{2} (t)}{2 u}$ , $u (0) = - 1$
72992	Solve the Differential Equation	(dy)/(dx)=4x-9 and y(5)=0	$\frac{d y}{d x} = 4 x - 9$ and $y (5) = 0$
72993	Solve the Differential Equation	(dy)/(dx)=x/(sin(y))-9/(sin(y))	$\frac{d y}{d x} = \frac{x}{\sin (y)} - \frac{9}{\sin (y)}$
72994	Solve the Differential Equation	(dT)/(dt)+kT=100k	$\frac{d T}{d t} + k T = 100 k$
72995	Solve the Differential Equation	x(dy)/(dx)+y=x	$x \frac{d y}{d x} + y = x$
72996	Solve the Differential Equation	x^2sin(xdx)+x(yd)y=0	$x^{2} \sin (x d x) + x yd y = 0$
72997	Solve the Differential Equation	8y(dy)/(dx)=x	$8 y \frac{d y}{d x} = x$
72998	Solve the Differential Equation	(dy)/(dx)=(-xy^2)/2	$\frac{d y}{d x} = \frac{- x y^{2}}{2}$
72999	Solve the Differential Equation	(dx)/(dy)=(1+2y^2)/(ysin(x))	$\frac{d x}{d y} = \frac{1 + 2 y^{2}}{y \sin (x)}$
73000	Solve the Differential Equation	(x+1)(dy)/(dx)-2y=(x+1)^4	$(x + 1) \frac{d y}{d x} - 2 y = {(x + 1)}^{4}$