Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
73301	Solve the Differential Equation	f(x) = square root of 2x-3	$f (x) = \sqrt{2 x - 3}$
73302	Solve the Differential Equation	(dy)/(dx)+(2y)/x=(x-1)y^2	$\frac{d y}{d x} + \frac{2 y}{x} = (x - 1) y^{2}$
73303	Solve the Differential Equation	(dr)/(dtheta)=picos(pitheta) , r(0)=2	$\frac{d r}{d θ} = π \cos (π θ)$ , $r (0) = 2$
73304	Solve the Differential Equation	(dr)/(ds)=0.9r	$\frac{d r}{d s} = 0.9 r$
73305	Solve the Differential Equation	(dy)/(dx)+(tan(x))y=sin(x)	$\frac{d y}{d x} + (\tan (x)) y = \sin (x)$
73306	Solve the Differential Equation	(dy)/(dx)=(x^2+x)/(y+3)	$\frac{d y}{d x} = \frac{x^{2} + x}{y + 3}$
73307	Solve the Differential Equation	(dy)/(dx)=(1+y)/x	$\frac{d y}{d x} = \frac{(1 + y)}{x}$
73308	Solve the Differential Equation	(ds)/(dt)=12t(3t^2-1)^3 , s(1)=15	$\frac{d s}{d t} = 12 t {(3 t^{2} - 1)}^{3}$ , $s (1) = 15$
73309	Solve the Differential Equation	(dy)/(dx)+1/(x-5)y=(x-5)^2	$\frac{d y}{d x} + \frac{1}{x - 5} y = {(x - 5)}^{2}$
73310	Solve the Differential Equation	y''''+2y=3	$y'' + 2 y = 3$
73311	Solve the Differential Equation	(dy)/(dx)=5x^(2/3)	$\frac{d y}{d x} = 5 x^{\frac{2}{3}}$
73312	Solve the Differential Equation	xy^2dy-y^3dx+yx^2dx-x^3dy=0	$x y^{2} d y - y^{3} d x + y x^{2} d x - x^{3} d y = 0$
73313	Solve the Differential Equation	(dy)/(dx)=(x-y)/(x-y+1)	$\frac{d y}{d x} = \frac{x - y}{x - y + 1}$
73314	Solve the Differential Equation	y^2dx+(x^2-xy-y^2)dy=0	$y^{2} d x + (x^{2} - x y - y^{2}) d y = 0$
73315	Solve the Differential Equation	y'''' = square root of 1-y^2	$y'' = \sqrt{1 - y^{2}}$
73316	Solve the Differential Equation	(dr)/(dtheta)=picos(pitheta) , r(1)=2	$\frac{d r}{d θ} = π \cos (π θ)$ , $r (1) = 2$
73317	Solve the Differential Equation	(1+y^2)dx+x(yd)y=0	$(1 + y^{2}) d x + x yd y = 0$
73318	Solve the Differential Equation	x(yd)x+(x^2+y^2)dy=0	$x yd x + (x^{2} + y^{2}) d y = 0$
73319	Solve the Differential Equation	xdy+(2y-10x^2)dx=0	$x d y + (2 y - 10 x^{2}) d x = 0$
73320	Solve the Differential Equation	(x-3y)dx+(3x+y)dy=0	$(x - 3 y) d x + (3 x + y) d y = 0$
73321	Solve the Differential Equation	(dr)/(dp)=4sin(p)	$\frac{d r}{d p} = 4 \sin (p)$
73322	Solve the Differential Equation	(dy)/(dx)=(3x^2+4x-4)/(2y-4)	$\frac{d y}{d x} = \frac{3 x^{2} + 4 x - 4}{2 y - 4}$
73323	Solve the Differential Equation	(-2y^3+1)dx+(3xy^2+x^3)dy=0	$(- 2 y^{3} + 1) d x + (3 x y^{2} + x^{3}) d y = 0$
73324	Solve the Differential Equation	(dy)/(dx)=x-2	$\frac{d y}{d x} = x - 2$
73325	Solve the Differential Equation	3x(xy-3)dx+(x^2+2y)dy=0	$3 x (x y - 3) d x + (x^{2} + 2 y) d y = 0$
73326	Solve the Differential Equation	y''''+x/y=0	$y'' + \frac{x}{y} = 0$
73327	Solve the Differential Equation	(ds)/(dt)=8sin(t+pi/12)^2 , s(0)=9	$\frac{d s}{d t} = 8 \sin^{2} (t + \frac{π}{12})$ , $s (0) = 9$
73328	Solve the Differential Equation	x(dy)/(dx)=5x^3+4	$x \frac{d y}{d x} = 5 x^{3} + 4$
73329	Solve the Differential Equation	(2x-5y+3)dx-(2x+4y-6)dy=0	$(2 x - 5 y + 3) d x - (2 x + 4 y - 6) d y = 0$
73330	Solve the Differential Equation	(dy)/(dx)=1/x-sec(7x)^2	$\frac{d y}{d x} = \frac{1}{x} - \sec^{2} (7 x)$
73331	Solve the Differential Equation	(3x^2-x)dx-(dy)/y=0	$(3 x^{2} - x) d x - \frac{d y}{y} = 0$
73332	Solve the Differential Equation	(x^2+y)dx+(x-2y)dy=0	$(x^{2} + y) d x + (x - 2 y) d y = 0$
73333	Solve the Differential Equation	(xy+y^2)(dy)/(dx)=y^2	$(x y + y^{2}) \frac{d y}{d x} = y^{2}$
73334	Solve the Differential Equation	2(yd)x+x(x^2 natural log of y-1)dy=0	$2 yd x + x (x^{2} \ln (y) - 1) d y = 0$
73335	Solve the Differential Equation	(dy)/(dx)=e^(0.02x)	$\frac{d y}{d x} = e^{0.02 x}$
73336	Solve the Differential Equation	(dy)/(dx)=(5e^x)/(e^y)	$\frac{d y}{d x} = \frac{5 e^{x}}{e^{y}}$
73337	Solve the Differential Equation	(dy)/(dx)=-x ; integrated	$\frac{d y}{d x} = - x$ ; integrated
73338	Solve the Differential Equation	(6xy-y^3)dx+(4y+3x^2-3xy^2)dy=0	$(6 x y - y^{3}) d x + (4 y + 3 x^{2} - 3 x y^{2}) d y = 0$
73339	Solve the Differential Equation	(dy)/(dx)=-2x+3x^3	$\frac{d y}{d x} = - 2 x + 3 x^{3}$
73340	Solve the Differential Equation	(dY)/(du)=9/4u^(5/4)	$\frac{d Y}{d u} = \frac{9}{4} u^{\frac{5}{4}}$
73341	Solve the Differential Equation	(dy)/(dx)=4-x	$\frac{d y}{d x} = 4 - x$
73342	Solve the Differential Equation	xy^2dx-x^2y^2dy=0	$x y^{2} d x - x^{2} y^{2} d y = 0$
73343	Solve the Differential Equation	(1+x)(dy)/(dx)=4y	$(1 + x) \frac{d y}{d x} = 4 y$
73344	Solve the Differential Equation	square root of 1-9x^2y''''=x	$\sqrt{1 - 9 x^{2}} y'' = x$
73345	Solve the Differential Equation	(e^x-y)dx-(e^y-x)dy=0	$(e^{x} - y) d x - (e^{y} - x) d y = 0$
73346	Solve the Differential Equation	y''''''''-1/x=0	$y'''' - \frac{1}{x} = 0$
73347	Solve the Differential Equation	(dy)/(dx)=(-x)/(ye^(x^2))	$\frac{d y}{d x} = \frac{- x}{y e^{x^{2}}}$
73348	Solve the Differential Equation	(ds)/(dt)=8sin(t-pi/12)^2 , s(0)=4	$\frac{d s}{d t} = 8 \sin^{2} (t - \frac{π}{12})$ , $s (0) = 4$
73349	Solve the Differential Equation	(dy)/(dx)=(x^2)/3	$\frac{d y}{d x} = \frac{x^{2}}{3}$
73350	Solve the Differential Equation	y''''=xy+x-2y-2	$y'' = x y + x - 2 y - 2$
73351	Solve the Differential Equation	(dy)/(dx)=1+4y^2	$\frac{d y}{d x} = 1 + 4 y^{2}$
73352	Solve the Differential Equation	y(dx)/(dy)-x=2y^2 , y(1)=5	$y \frac{d x}{d y} - x = 2 y^{2}$ , $y (1) = 5$
73353	Solve the Differential Equation	y''''+2xy=2xe^(-x^2)	$y'' + 2 x y = 2 x e^{- x^{2}}$
73354	Solve the Differential Equation	y''''+2xy=23x	$y'' + 2 x y = 23 x$
73355	Solve the Differential Equation	(ds)/(dt)=cos(t)-sin(t) , s(pi/2)=8	$\frac{d s}{d t} = \cos (t) - \sin (t)$ , $s (\frac{π}{2}) = 8$
73356	Solve the Differential Equation	(dy)/(dx)+1/xy=1/(x^2)	$\frac{d y}{d x} + \frac{1}{x} y = \frac{1}{x^{2}}$
73357	Solve the Differential Equation	x^-2y^-5dx+x^-3y^-4dy=0	$x^{- 2} y^{- 5} d x + x^{- 3} y^{- 4} d y = 0$
73358	Solve the Differential Equation	(dy)/(dx)=x^3 , y(-1)=2	$\frac{d y}{d x} = x^{3}$ , $y (- 1) = 2$
73359	Solve the Differential Equation	2(yd)x+3xdy=0	$2 yd x + 3 x d y = 0$
73360	Solve the Differential Equation	(2x+3)dx+(x^2-1)dy=0	$(2 x + 3) d x + (x^{2} - 1) d y = 0$
73361	Solve the Differential Equation	e^(-y)((dy)/(dx)+1)=xe^x	$e^{- y} (\frac{d y}{d x} + 1) = x e^{x}$
73362	Solve the Differential Equation	(dy)/(dx)=-6x^5e^(-x^6)	$\frac{d y}{d x} = - 6 x^{5} e^{- x^{6}}$
73363	Solve the Differential Equation	(dy)/(dx)+4/xy=x^3y^2	$\frac{d y}{d x} + \frac{4}{x} y = x^{3} y^{2}$
73364	Solve the Differential Equation	(x+y)dxdy=0	$(x + y) d x d y = 0$
73365	Solve the Differential Equation	square root of x(dy)/(dx)=e^(7y+ square root of x)	$\sqrt{x} \frac{d y}{d x} = e^{7 y + \sqrt{x}}$
73366	Solve the Differential Equation	(x^3+y^2 square root of x^2+y^2)dx-xy square root of x^2+y^2dy=0	$(x^{3} + y^{2} \sqrt{x^{2} + y^{2}}) d x - x y \sqrt{x^{2} + y^{2}} d y = 0$
73367	Solve the Differential Equation	(dy)/(dx)=2xy-x	$\frac{d y}{d x} = 2 x y - x$
73368	Solve the Differential Equation	(dy)/(dx)=( square root of x)/xi	$\frac{d y}{d x} = \frac{\sqrt{x}}{x} i$
73369	Solve the Differential Equation	(x-y^2)dx+2x(yd)y=0	$(x - y^{2}) d x + 2 x yd y = 0$
73370	Solve the Differential Equation	(dy)/(dx)=3e^(-3x)	$\frac{d y}{d x} = 3 e^{- 3 x}$
73371	Solve the Differential Equation	y''''=1-y	$y'' = 1 - y$
73372	Solve the Differential Equation	x(dy)/(dx)=3-y	$x \frac{d y}{d x} = 3 - y$
73373	Solve the Differential Equation	natural log of x(dx)/(dy)=x/y	$\ln (x) \frac{d x}{d y} = \frac{x}{y}$
73374	Solve the Differential Equation	(dy)/(dx)=x+xy^2	$\frac{d y}{d x} = x + x y^{2}$
73375	Solve the Differential Equation	(x^2+1)(dy)/(dx)+3xy=6x	$(x^{2} + 1) \frac{d y}{d x} + 3 x y = 6 x$
73376	Solve the Differential Equation	(dy)/(dx)+4y=4/3	$\frac{d y}{d x} + 4 y = \frac{4}{3}$
73377	Solve the Differential Equation	(dy)/(dx)=3x+2y	$\frac{d y}{d x} = 3 x + 2 y$
73378	Solve the Differential Equation	(x^2+1)(y^3-1)dx=x^2y^2dy	$(x^{2} + 1) (y^{3} - 1) d x = x^{2} y^{2} d y$
73379	Solve the Differential Equation	(dy)/(dx)=25e^(-5x)	$\frac{d y}{d x} = 25 e^{- 5 x}$
73380	Solve the Differential Equation	2(dy)/(dt)-y=4sin(3t)	$2 \frac{d y}{d t} - y = 4 \sin (3 t)$
73381	Solve the Differential Equation	y''''-y=x	$y'' - y = x$
73382	Solve the Differential Equation	(y^2-y)(dy)/(dx)=x+ natural log of x	$(y^{2} - y) \frac{d y}{d x} = x + \ln (x)$
73383	Solve the Differential Equation	(dy)/(dx)=e^(0.04x)	$\frac{d y}{d x} = e^{0.04 x}$
73384	Solve the Differential Equation	(dy)/(dx)=-3x^2y	$\frac{d y}{d x} = - 3 x^{2} y$
73385	Solve the Differential Equation	(dy)/(dx)=(3y)/(2x+1)	$\frac{d y}{d x} = \frac{3 y}{2 x + 1}$
73386	Solve the Differential Equation	(dy)/(dx)=x-4xy	$\frac{d y}{d x} = x - 4 x y$
73387	Solve the Differential Equation	(dy)/(dx)=-8x+6x^2	$\frac{d y}{d x} = - 8 x + 6 x^{2}$
73388	Solve the Differential Equation	(dW)/(dh)=0.0012h^2	$\frac{d W}{d h} = 0.0012 h^{2}$
73389	Solve the Differential Equation	yy''''''''+2(y'''')^2=0	$y y'''' + 2 {(y'')}^{2} = 0$
73390	Solve the Differential Equation	(ds)/(dt)=8sin(t+pi/12)^2 , s(0)=2	$\frac{d s}{d t} = 8 \sin^{2} (t + \frac{π}{12})$ , $s (0) = 2$
73391	Solve the Differential Equation	(dy)/(dt)+50y=0	$\frac{d y}{d t} + 50 y = 0$
73392	Solve the Differential Equation	y''''''''+5y=0	$y'''' + 5 y = 0$
73393	Solve the Differential Equation	(dy)/(dx)=3x^2+y^2	$\frac{d y}{d x} = 3 x^{2} + y^{2}$
73394	Solve the Differential Equation	(dy)/(dx)=20e^(-4x)	$\frac{d y}{d x} = 20 e^{- 4 x}$
73395	Solve the Differential Equation	(dy)/(dx)+xy=2x	$\frac{d y}{d x} + x y = 2 x$
73396	Solve the Differential Equation	f(x) = natural log of 1+x^2	$f (x) = \ln (1 + x^{2})$
73397	Solve the Differential Equation	(dy)/(dx)=(xy)/( natural log of y)	$\frac{d y}{d x} = \frac{x y}{\ln (y)}$
73398	Solve the Differential Equation	(dy)/(dx)=1/2 square root of ycos( square root of y)^2	$\frac{d y}{d x} = \frac{1}{2} \sqrt{y} \cos^{2} (\sqrt{y})$
73399	Solve the Differential Equation	(dy)/(dx)=2x+5	$\frac{d y}{d x} = 2 x + 5$
73400	Solve the Differential Equation	square root of x(dy)/(dx)=e^(5y+ square root of x)	$\sqrt{x} \frac{d y}{d x} = e^{5 y + \sqrt{x}}$