Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
71901	Solve the Differential Equation	x(y-1)dx+(x+1)dy=0	$x (y - 1) d x + (x + 1) d y = 0$
71902	Solve the Differential Equation	(dy)/(dx)=9xe^y	$\frac{d y}{d x} = 9 x e^{y}$
71903	Solve the Differential Equation	(x-y+1)dx-(x+y-3)dy=0	$(x - y + 1) d x - (x + y - 3) d y = 0$
71904	Solve the Differential Equation	(dy)/(dx)-2xy+x=0	$\frac{d y}{d x} - 2 x y + x = 0$
71905	Solve the Differential Equation	dx-1/(1+y^2)dy=0	$d x - \frac{1}{1 + y^{2}} d y = 0$
71906	Solve the Differential Equation	5 square root of xy(dy)/(dx)=2	$5 \sqrt{x y} \frac{d y}{d x} = 2$
71907	Solve the Differential Equation	(dy)/(dx)=-6xy	$\frac{d y}{d x} = - 6 x y$
71908	Solve the Differential Equation	(dy)/(dx)=(sec(y))/x	$\frac{d y}{d x} = \frac{(\sec (y))}{x}$
71909	Solve the Differential Equation	7 square root of xy(dy)/(dx)=4	$7 \sqrt{x y} \frac{d y}{d x} = 4$
71910	Solve the Differential Equation	(dx)/(dy)=(x^2y^2)/(1+x)	$\frac{d x}{d y} = \frac{x^{2} y^{2}}{1 + x}$
71911	Solve the Differential Equation	(dy)/(dx)=(x+1)/(y^4+1)	$\frac{d y}{d x} = \frac{x + 1}{y^{4} + 1}$
71912	Solve the Differential Equation	(d^2y)/(dx^2)-4y=0	$\frac{d^{2} y}{d x^{2}} - 4 y = 0$
71913	Solve the Differential Equation	(dy)/(dx)=e^(0.1x)	$\frac{d y}{d x} = e^{0.1 x}$
71914	Solve the Differential Equation	(dy)/(dx)=11/x	$\frac{d y}{d x} = \frac{11}{x}$
71915	Solve the Differential Equation	(t^2+1)dt+(y^2+y)dy=0	$(t^{2} + 1) d t + (y^{2} + y) d y = 0$
71916	Solve the Differential Equation	(ds)/(dt)=36t(9t^2-7)^3 , s(1)=9	$\frac{d s}{d t} = 36 t {(9 t^{2} - 7)}^{3}$ , $s (1) = 9$
71917	Solve the Differential Equation	xdx+1/ydy=0	$x d x + \frac{1}{y} d y = 0$
71918	Solve the Differential Equation	(dy)/(dx)-xy=x	$\frac{d y}{d x} - x y = x$
71919	Solve the Differential Equation	(dy)/(dx)=(sin(x))/(e^y)	$\frac{d y}{d x} = \frac{\sin (x)}{e^{y}}$
71920	Solve the Differential Equation	(dy)/(dx)-y=0	$\frac{d y}{d x} - y = 0$
71921	Solve the Differential Equation	(dy)/(dx)=9xe^y , y(0)=0	$\frac{d y}{d x} = 9 x e^{y}$ , $y (0) = 0$
71922	Solve the Differential Equation	y(dx)/(dy)-x=2y^2	$y \frac{d x}{d y} - x = 2 y^{2}$
71923	Solve the Differential Equation	(t^2-2ty+3y^2)dt+(y^2+6ty-t^2)dy=0	$(t^{2} - 2 t y + 3 y^{2}) d t + (y^{2} + 6 t y - t^{2}) d y = 0$
71924	Solve the Differential Equation	(dy)/(dx)+xy=x^3	$\frac{d y}{d x} + x y = x^{3}$
71925	Solve the Differential Equation	(dy)/(dx)=y(1-y)	$\frac{d y}{d x} = y (1 - y)$
71926	Solve the Differential Equation	(1+x^4)(dy)/(dx)=(x^3)/y	$(1 + x^{4}) \frac{d y}{d x} = \frac{x^{3}}{y}$
71927	Solve the Differential Equation	(dy)/(dx)=32x	$\frac{d y}{d x} = 32 x$
71928	Solve the Differential Equation	(dy)/(dx)=6e^(x-y)	$\frac{d y}{d x} = 6 e^{x - y}$
71929	Solve the Differential Equation	(dy)/(dx)=7x^2y	$\frac{d y}{d x} = 7 x^{2} y$
71930	Solve the Differential Equation	y^2(dy)/(dx)=3x^2y^3-6x^2	$y^{2} \frac{d y}{d x} = 3 x^{2} y^{3} - 6 x^{2}$
71931	Solve the Differential Equation	(yx-y)dy-(y+1)dx=0	$(y x - y) d y - (y + 1) d x = 0$
71932	Solve the Differential Equation	v^2dx+x(x+v)dv=0	$v^{2} d x + x (x + v) d v = 0$
71933	Solve the Differential Equation	f(x)=(ax+b)/(cx+d)	$f (x) = \frac{a x + b}{c x + d}$
71934	Solve the Differential Equation	(dy)/(dx)=-(x+6)/(7y^2)	$\frac{d y}{d x} = - \frac{x + 6}{7 y^{2}}$
71935	Solve the Differential Equation	y''''=2xy^2	$y'' = 2 x y^{2}$
71936	Solve the Differential Equation	(dy)/(dx)=8sin(3x)	$\frac{d y}{d x} = 8 \sin (3 x)$
71937	Solve the Differential Equation	square root of y^2+1dx-x(yd)y=0	$\sqrt{y^{2} + 1} d x - x yd y = 0$
71938	Solve the Differential Equation	(dy)/(dx)=-2x+6x^2	$\frac{d y}{d x} = - 2 x + 6 x^{2}$
71939	Solve the Differential Equation	y^3dx+2(x^3-xy^2)dy=0	$y^{3} d x + 2 (x^{3} - x y^{2}) d y = 0$
71940	Solve the Differential Equation	xy''''+y=e^x	$x y'' + y = e^{x}$
71941	Solve the Differential Equation	(2x+3)y=(dy)/(dx)	$(2 x + 3) y = \frac{d y}{d x}$
71942	Solve the Differential Equation	y''''+2y=e^x	$y'' + 2 y = e^{x}$
71943	Solve the Differential Equation	(dy)/(dx)+x=2y	$\frac{d y}{d x} + x = 2 y$
71944	Solve the Differential Equation	(x^2+1)(dy)/(dx)-2xy-2x=0	$(x^{2} + 1) \frac{d y}{d x} - 2 x y - 2 x = 0$
71945	Solve the Differential Equation	(dy)/(dx)=-3/x	$\frac{d y}{d x} = - \frac{3}{x}$
71946	Solve the Differential Equation	y''''''''+2y''''=0	$y'''' + 2 y'' = 0$
71947	Solve the Differential Equation	(dy)/(dx)=(x^2)/9+7/9	$\frac{d y}{d x} = \frac{x^{2}}{9} + \frac{7}{9}$
71948	Solve the Differential Equation	(xy+3)dx+(2x-y^2+1)dy=0	$(x y + 3) d x + (2 x - y^{2} + 1) d y = 0$
71949	Solve the Differential Equation	(dy)/(dx)=(sin(x))/(cos(y))	$\frac{d y}{d x} = \frac{\sin (x)}{\cos (y)}$
71950	Solve the Differential Equation	(x-y)dx+y^2dy=0	$(x - y) d x + y^{2} d y = 0$
71951	Solve the Differential Equation	(dy)/(dx)=-10y	$\frac{d y}{d x} = - 10 y$
71952	Solve the Differential Equation	(dy)/(dx)+4y=8	$\frac{d y}{d x} + 4 y = 8$
71953	Solve the Differential Equation	yy''''=x	$y y'' = x$
71954	Solve the Differential Equation	(dy)/(dx)=(x+1)(y-1)	$\frac{d y}{d x} = (x + 1) (y - 1)$
71955	Solve the Differential Equation	(dy)/(dx)=2x+3 , y(1)=-2	$\frac{d y}{d x} = 2 x + 3$ , $y (1) = - 2$
71956	Solve the Differential Equation	y''''=8y	$y'' = 8 y$
71957	Solve the Differential Equation	x^2yy''''=e^y	$x^{2} y y'' = e^{y}$
71958	Solve the Differential Equation	(dy)/(dt)+2y=1	$\frac{d y}{d t} + 2 y = 1$
71959	Solve the Differential Equation	y''''=-y/x	$y'' = - \frac{y}{x}$
71960	Solve the Differential Equation	(x-y natural log of y+y natural log of x)dx+x( natural log of y- natural log of x)dy=0	$(x - y \ln (y) + y \ln (x)) d x + x (\ln (y) - \ln (x)) d y = 0$
71961	Solve the Differential Equation	(x+y)dx-2(yd)y=0	$(x + y) d x - 2 yd y = 0$
71962	Solve the Differential Equation	(dy)/(dx)=8e^(x-y)	$\frac{d y}{d x} = 8 e^{x - y}$
71963	Solve the Differential Equation	(dy)/(dx)=4x^3y-6x^2y	$\frac{d y}{d x} = 4 x^{3} y - 6 x^{2} y$
71964	Solve the Differential Equation	3(dy)/(dx)-21xy-7x=0	$3 \frac{d y}{d x} - 21 x y - 7 x = 0$
71965	Solve the Differential Equation	y(y+2x-2)dx-2(x+y)dy=0	$y (y + 2 x - 2) d x - 2 (x + y) d y = 0$
71966	Solve the Differential Equation	(dy)/(dx)=4cos(5x)	$\frac{d y}{d x} = 4 \cos (5 x)$
71967	Solve the Differential Equation	(dy)/(dx)=-xy	$\frac{d y}{d x} = - x y$
71968	Solve the Differential Equation	(dy)/(dx)=x^2-2x+4	$\frac{d y}{d x} = x^{2} - 2 x + 4$
71969	Solve the Differential Equation	(dy)/(dx)=-2xy^4	$\frac{d y}{d x} = - 2 x y^{4}$
71970	Solve the Differential Equation	(dy)/(dx)+2y=e^(-x)	$\frac{d y}{d x} + 2 y = e^{- x}$
71971	Solve the Differential Equation	y''''+2xy=6x	$y'' + 2 x y = 6 x$
71972	Solve the Differential Equation	(dy)/(dx)+2y=2e^x	$\frac{d y}{d x} + 2 y = 2 e^{x}$
71973	Solve the Differential Equation	csc(ydx)+sec(xdy)^2=0	$\csc (yd x) + \sec^{2} (x d y) = 0$
71974	Solve the Differential Equation	y''''=-2y	$y'' = - 2 y$
71975	Solve the Differential Equation	(dy)/(dx)=2x-5 , y(1)=-2	$\frac{d y}{d x} = 2 x - 5$ , $y (1) = - 2$
71976	Solve the Differential Equation	(dy)/(dx)=(x^2+y^2)/(2xy)	$\frac{d y}{d x} = \frac{x^{2} + y^{2}}{2 x y}$
71977	Solve the Differential Equation	xy''''+y=x^2	$x y'' + y = x^{2}$
71978	Solve the Differential Equation	(dy)/(dx)=x/(7cos(y))	$\frac{d y}{d x} = \frac{x}{7 \cos (y)}$
71979	Solve the Differential Equation	(y^2+xy^2)y''''=1	$(y^{2} + x y^{2}) y'' = 1$
71980	Solve the Differential Equation	y''''-2y''''+10y=0	$y'' - 2 y'' + 10 y = 0$
71981	Solve the Differential Equation	y''''=4-9x^2-6x^5	$y'' = 4 - 9 x^{2} - 6 x^{5}$
71982	Solve the Differential Equation	2xy''''+y=4x	$2 x y'' + y = 4 x$
71983	Solve the Differential Equation	2xy*(dy)/(dx)=1+y^2	$2 x y \cdot \frac{d y}{d x} = 1 + y^{2}$
71984	Solve the Differential Equation	2(yd)x=(x^2-1)(dx-dy)	$2 yd x = (x^{2} - 1) (d x - d y)$
71985	Solve the Differential Equation	y''''=2x+3y-1	$y'' = 2 x + 3 y - 1$
71986	Solve the Differential Equation	(xy^2+y-x)dx+x(xy+1)dy=0	$(x y^{2} + y - x) d x + x (x y + 1) d y = 0$
71987	Solve the Differential Equation	(dy)/(dt)-yt=t	$\frac{d y}{d t} - y t = t$
71988	Solve the Differential Equation	y''''=-2xy	$y'' = - 2 x y$
71989	Solve the Differential Equation	(dy)/(dx)=3x^-4	$\frac{d y}{d x} = 3 x^{- 4}$
71990	Solve the Differential Equation	(dy)/(dx)=cos(x+4)	$\frac{d y}{d x} = \cos (x + 4)$
71991	Solve the Differential Equation	(dy)/(dx)=(8x)/y	$\frac{d y}{d x} = \frac{8 x}{y}$
71992	Solve the Differential Equation	y^2dx+(2x-3y)dy=0	$y^{2} d x + (2 x - 3 y) d y = 0$
71993	Solve the Differential Equation	ydx=2(x+y)dy	$yd x = 2 (x + y) d y$
71994	Solve the Differential Equation	(3x^2+y)dx+(x^2y-x)dy=0	$(3 x^{2} + y) d x + (x^{2} y - x) d y = 0$
71995	Solve the Differential Equation	(dy)/(dx)=9/x	$\frac{d y}{d x} = \frac{9}{x}$
71996	Solve the Differential Equation	y''''''''''''+3y''''''''+3y''''+y=0	$y'''''' + 3 y'''' + 3 y'' + y = 0$
71997	Solve the Differential Equation	(dy)/(dt)=t/(t^2y+y)	$\frac{d y}{d t} = \frac{t}{t^{2} y + y}$
71998	Solve the Differential Equation	(dy)/(dx)=y^-1x^-3	$\frac{d y}{d x} = y^{- 1} x^{- 3}$
71999	Solve the Differential Equation	(dN)/(dt)=-kN	$\frac{d N}{d t} = - k N$
72000	Solve the Differential Equation	(dR)/(dt)=13.897t+284.653/t	$\frac{d R}{d t} = 13.897 t + \frac{284.653}{t}$