Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
79901	Solve the Differential Equation	(x+1)y''''''''-(2-x)y''''+y=0	$(x + 1) y'''' - (2 - x) y'' + y = 0$
79902	Verify the Differential Equation Solution	(dy)/(dx)=1/( square root of 36-x^2) , y(0)=pi	$\frac{d y}{d x} = \frac{1}{\sqrt{36 - x^{2}}}$ , $y (0) = π$
79903	Solve the Differential Equation	y''''''''=25y	$y'''' = 25 y$
79904	Solve the Differential Equation	(dy)/(dx)=x^3-b^2x	$\frac{d y}{d x} = x^{3} - b^{2} x$
79905	Solve the Differential Equation	(dy)/(dx)=20x^3	$\frac{d y}{d x} = 20 x^{3}$
79906	Solve the Differential Equation	f(x)=x^3-2x+1	$f (x) = x^{3} - 2 x + 1$
79907	Solve the Differential Equation	(dy)/(dx)-y=e^(-x)y^2	$\frac{d y}{d x} - y = e^{- x} y^{2}$
79908	Solve the Differential Equation	(1+3xsin(y))dx-x^2cos(ydy)=0	$(1 + 3 x \sin (y)) d x - x^{2} \cos (yd y) = 0$
79909	Solve the Differential Equation	(d^2y)/(dx^2)-6(dy)/(dx)+13y=0	$\frac{d^{2} y}{d x^{2}} - 6 \frac{d y}{d x} + 13 y = 0$
79910	Solve the Differential Equation	y''''=(x^3+y^3)/(3xy^2)	$y'' = \frac{(x^{3} + y^{3})}{3 x y^{2}}$
79911	Solve the Differential Equation	cos(x)cos(ydy)-sin(x)sin(ydx)=0	$\cos (x) \cos (yd y) - \sin (x) \sin (yd x) = 0$
79912	Solve the Differential Equation	y''''=5y^2x	$y'' = 5 y^{2} x$
79913	Solve the Differential Equation	x((dy)/(dx))-2y=x^3cos(4x)	$x (\frac{d y}{d x}) - 2 y = x^{3} \cos (4 x)$
79914	Solve the Differential Equation	(dy)/(dt)=y^4	$\frac{d y}{d t} = y^{4}$
79915	Solve the Differential Equation	(x+7)y''''=9y	$(x + 7) y'' = 9 y$
79916	Solve the Differential Equation	2x(dy)/(dx)- natural log of x^2=0	$2 x \frac{d y}{d x} - \ln (x^{2}) = 0$
79917	Solve the Differential Equation	(x^5+3y)/x-(dy)/(dx)=0	$\frac{x^{5} + 3 y}{x} - \frac{d y}{d x} = 0$
79918	Solve the Differential Equation	y''''''''-6y''''+5y=3cos(x)	$y'''' - 6 y'' + 5 y = 3 \cos (x)$
79919	Solve the Differential Equation	(dy)/(dx)=(y+1)/(1+x)	$\frac{d y}{d x} = \frac{y + 1}{1 + x}$
79920	Solve the Differential Equation	(dy)/(dx)=4x^3y-y	$\frac{d y}{d x} = 4 x^{3} y - y$
79921	Solve the Differential Equation	(dy)/(dt)=6-y	$\frac{d y}{d t} = 6 - y$
79922	Solve the Differential Equation	y(1+xy)dx-xdy=0	$y (1 + x y) d x - x d y = 0$
79923	Solve the Differential Equation	(2x+y-2)-(y-x-2)(dy)/(dx)=0	$(2 x + y - 2) - (y - x - 2) \frac{d y}{d x} = 0$
79924	Solve the Differential Equation	(dy)/(dx)=(27-9x^2)/( square root of x^3-9x+2)	$\frac{d y}{d x} = \frac{27 - 9 x^{2}}{\sqrt{x^{3} - 9 x + 2}}$
79925	Solve the Differential Equation	2y(x^2+1)dx+((x^3)/3+x)dy=0	$2 y (x^{2} + 1) d x + (\frac{x^{3}}{3} + x) d y = 0$
79926	Solve the Differential Equation	(dy)/(dx)=-8x^7e^(-x^8) , y(0)=8	$\frac{d y}{d x} = - 8 x^{7} e^{- x^{8}}$ , $y (0) = 8$
79927	Solve the Differential Equation	x(dy)/(dx)=y+y^3cos(x)	$x \frac{d y}{d x} = y + y^{3} \cos (x)$
79928	Solve the Differential Equation	dx+(1-x)dy=0	$d x + (1 - x) d y = 0$
79929	Solve the Differential Equation	f(x)=x(\|x\|-1)	$f (x) = x (\| x \| - 1)$
79930	Solve the Differential Equation	(dy)/(dx)=4x^(5/8)	$\frac{d y}{d x} = 4 x^{\frac{5}{8}}$
79931	Solve the Differential Equation	y'''' square root of 1+x^3=x^2y+x^2	$y'' \sqrt{1 + x^{3}} = x^{2} y + x^{2}$
79932	Solve the Differential Equation	3y''''+12y=4	$3 y'' + 12 y = 4$
79933	Solve the Differential Equation	(dy)/(dx)=y(xy^7-1)	$\frac{d y}{d x} = y (x y^{7} - 1)$
79934	Solve the Differential Equation	y''''-y''''+12*y=0	$y'' - y'' + 12 \cdot y = 0$
79935	Solve the Differential Equation	(dy)/(dx)=x(2x-1)^5	$\frac{d y}{d x} = x {(2 x - 1)}^{5}$
79936	Solve the Differential Equation	y''''-3y=9	$y'' - 3 y = 9$
79937	Solve the Differential Equation	(dx)/(dy)=8x	$\frac{d x}{d y} = 8 x$
79938	Solve the Differential Equation	(dy)/(dx)=x^5+x^6 , y(1)=2	$\frac{d y}{d x} = x^{5} + x^{6}$ , $y (1) = 2$
79939	Solve the Differential Equation	(dy)/(dx)=-4x^2y	$\frac{d y}{d x} = - 4 x^{2} y$
79940	Solve the Differential Equation	y''''''''-y=cosh(x)	$y'''' - y = \cosh (x)$
79941	Solve the Differential Equation	(dy)/(dx)=(x+1)y^2	$\frac{d y}{d x} = (x + 1) y^{2}$
79942	Solve the Differential Equation	(dy)/(dx)=y(5x^2+4)	$\frac{d y}{d x} = y (5 x^{2} + 4)$
79943	Solve the Differential Equation	(1+x)y''''+y=cos(x)	$(1 + x) y'' + y = \cos (x)$
79944	Solve the Differential Equation	y''''''''+4y=4sin(2x)	$y'''' + 4 y = 4 \sin (2 x)$
79945	Solve the Differential Equation	(1+2y)dx+(x-4)dy=0	$(1 + 2 y) d x + (x - 4) d y = 0$
79946	Solve the Differential Equation	(dy)/(dx)=cos(x) , y(0)=1	$\frac{d y}{d x} = \cos (x)$ , $y (0) = 1$
79947	Solve the Differential Equation	1/(x+1)(dy)/(dx)=y+2	$\frac{1}{x + 1} \cdot \frac{d y}{d x} = y + 2$
79948	Solve the Differential Equation	e^(x-y)dx+e^(y-x)dy=0	$e^{x - y} d x + e^{y - x} d y = 0$
79949	Solve the Differential Equation	(dy)/(dx)=6x^2-4x+3	$\frac{d y}{d x} = 6 x^{2} - 4 x + 3$
79950	Solve the Differential Equation	(dy)/(dx)-(2y)/x=(x^2)/(1+x^2)	$\frac{d y}{d x} - \frac{2 y}{x} = \frac{x^{2}}{1 + x^{2}}$
79951	Solve the Differential Equation	(dy)/(dx)=sin(x) , y(pi/2)=1	$\frac{d y}{d x} = \sin (x)$ , $y (\frac{π}{2}) = 1$
79952	Solve the Differential Equation	(dy)/(dx)=(y-2)^2-0.04	$\frac{d y}{d x} = {(y - 2)}^{2} - 0.04$
79953	Solve the Differential Equation	y-x(dy)/(dx)=6x^3	$y - x \frac{d y}{d x} = 6 x^{3}$
79954	Solve the Differential Equation	(dC)/(dx)=14/( cube root of 14x+3)	$\frac{d C}{d x} = \frac{14}{\sqrt[3]{14 x + 3}}$
79955	Solve the Differential Equation	ydx-xdy+x^3dx=2dx	$yd x - x d y + x^{3} d x = 2 d x$
79956	Solve the Differential Equation	y''''=(2x+y)^2	$y'' = {(2 x + y)}^{2}$
79957	Solve the Differential Equation	(dy)/(dx)=(8x^2)/( square root of 3+x^3)	$\frac{d y}{d x} = \frac{8 x^{2}}{\sqrt{3 + x^{3}}}$
79958	Solve the Differential Equation	(dy)/(dx)+3y=e^(-2x)	$\frac{d y}{d x} + 3 y = e^{- 2 x}$
79959	Solve the Differential Equation	y''''=(3x+y-1)^2	$y'' = {(3 x + y - 1)}^{2}$
79960	Solve the Differential Equation	(2y^2+4x)dx+3x(yd)y=0	$(2 y^{2} + 4 x) d x + 3 x yd y = 0$
79961	Solve the Differential Equation	x''''=x+y	$x'' = x + y$
79962	Solve the Differential Equation	(dy)/(dx)=(2x+1)/(y-3) ; , y(0)=4	$\frac{d y}{d x} = \frac{2 x + 1}{y - 3}$ ; , $y (0) = 4$
79963	Solve the Differential Equation	f(x)=x^2(x-3)^3	$f (x) = x^{2} {(x - 3)}^{3}$
79964	Solve the Differential Equation	y''''=2x+c_1	$y'' = 2 x + c_{1}$
79965	Solve the Differential Equation	f(x)=4x^5	$f (x) = 4 x^{5}$
79966	Solve the Differential Equation	x^2dy-x(yd)x=2(yd)x	$x^{2} d y - x yd x = 2 yd x$
79967	Solve the Differential Equation	sin(xdx)+cos(xdy)=0	$\sin (x d x) + \cos (x d y) = 0$
79968	Solve the Differential Equation	y''''=y/x+2x+1	$y'' = \frac{y}{x} + 2 x + 1$
79969	Solve the Differential Equation	f(x)=3x^3	$f (x) = 3 x^{3}$
79970	Solve the Differential Equation	(dy)/(dx)=2x^3 square root of y	$\frac{d y}{d x} = 2 x^{3} \sqrt{y}$
79971	Solve the Differential Equation	(dy)/(dx)-8-2x^2+4y^2+y^2x^2=0	$\frac{d y}{d x} - 8 - 2 x^{2} + 4 y^{2} + y^{2} x^{2} = 0$
79972	Solve the Differential Equation	(dy)/(dt)=9y+ty+cos(t)	$\frac{d y}{d t} = 9 y + t y + \cos (t)$
79973	Solve the Differential Equation	(dy)/(dx)+y/(x^2)-x^4=0	$\frac{d y}{d x} + \frac{y}{x^{2}} - x^{4} = 0$
79974	Solve the Differential Equation	(dP)/(dt)=c natural log of K/PP	$\frac{d P}{d t} = c \ln (\frac{K}{P}) P$
79975	Solve the Differential Equation	y''''=6/x	$y'' = \frac{6}{x}$
79976	Solve the Differential Equation	(x^2+2xy-4y^2)-(x^2-8xy-4y^2)dy=0	$(x^{2} + 2 x y - 4 y^{2}) - (x^{2} - 8 x y - 4 y^{2}) d y = 0$
79977	Solve the Differential Equation	dy/y+e^(cos(x))(sin(x))dx=0	$d \frac{y}{y} + e^{\cos (x)} (\sin (x)) d x = 0$
79978	Solve the Differential Equation	(dx)/(dt)=-5t	$\frac{d x}{d t} = - 5 t$
79979	Solve the Differential Equation	(dy)/(dx)=4x^2y-5xy	$\frac{d y}{d x} = 4 x^{2} y - 5 x y$
79980	Solve the Differential Equation	((d^2t)/(dx^2))^3+5x((dt)/(dx))^4-3=6cos(x)	${(\frac{d^{2} t}{d x^{2}})}^{3} + 5 x {(\frac{d t}{d x})}^{4} - 3 = 6 \cos (x)$
79981	Solve the Differential Equation	(e^(2x)+4)dy=ydx	$(e^{2 x} + 4) d y = yd x$
79982	Solve the Differential Equation	y''''=-2e^x+x^2-4	$y'' = - 2 e^{x} + x^{2} - 4$
79983	Solve the Differential Equation	y''''''''+2y''''=3	$y'''' + 2 y'' = 3$
79984	Solve the Differential Equation	y''''(y^2x+x^3)=1/(y^-3)	$y'' (y^{2} x + x^{3}) = \frac{1}{y^{- 3}}$
79985	Solve the Differential Equation	x(dz)/(dx)+z=0	$x \frac{d z}{d x} + z = 0$
79986	Solve the Differential Equation	2x(dy)/(dx)=xsin(2x)	$2 x \cdot \frac{d y}{d x} = x \cdot \sin (2 x)$
79987	Solve the Differential Equation	y(x^2-1)dy+x(y^2-1)dx=0	$y (x^{2} - 1) d y + x (y^{2} - 1) d x = 0$
79988	Solve the Differential Equation	(x-4)(dy)/(dx)+y=6e^x	$(x - 4) \frac{d y}{d x} + y = 6 e^{x}$
79989	Solve the Differential Equation	2yy''''(t)=3t^2	$2 y y'' (t) = 3 t^{2}$
79990	Solve the Differential Equation	1/y(dy)/(dt)=51/t	$\frac{1}{y} \cdot \frac{d y}{d t} = 5 \cdot \frac{1}{t}$
79991	Solve the Differential Equation	(arcsin(x))/ydx+(1-e^y)dy=0	$\frac{\arcsin (x)}{y} d x + (1 - e^{y}) d y = 0$
79992	Solve the Differential Equation	(dy)/(dx)-(y^2-1)/x=0	$\frac{d y}{d x} - \frac{y^{2} - 1}{x} = 0$
79993	Solve the Differential Equation	y(3+e^x)dy-3e^xdx=0	$y (3 + e^{x}) d y - 3 e^{x} d x = 0$
79994	Solve the Differential Equation	y(x^3y^3+2x^2-y)dx+x^3(xy^3-2)dy=0	$y (x^{3} y^{3} + 2 x^{2} - y) d x + x^{3} (x y^{3} - 2) d y = 0$
79995	Solve the Differential Equation	(dy)/(dx)=6x^5	$\frac{d y}{d x} = 6 x^{5}$
79996	Solve the Differential Equation	(dy)/(dx)=x^3-xy	$\frac{d y}{d x} = x^{3} - x y$
79997	Solve the Differential Equation	(dy)/(dx)=(x+y-4)^2	$\frac{d y}{d x} = {(x + y - 4)}^{2}$
79998	Solve the Differential Equation	(dy)/(dx)=(6x^5)/(3e^y)	$\frac{d y}{d x} = \frac{6 x^{5}}{3 e^{y}}$
79999	Solve the Differential Equation	y''''=(4y)/(3x)	$y'' = \frac{4 y}{3 x}$
80000	Solve the Differential Equation	x''''''''+4x=0	$x'''' + 4 x = 0$