Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
71301	Solve the Differential Equation	(dy)/(dx)=(sin(x))/(sin(x)-1)	$\frac{d y}{d x} = \frac{\sin (x)}{\sin (x) - 1}$
71302	Solve the Differential Equation	csc(ydx)+sec(xdy)^2=0	$\csc (yd x) + \sec^{2} (x d y) = 0$
71303	Solve the Differential Equation	y''''''''=0	$y'''' = 0$
71304	Solve the Differential Equation	(dy)/(dx)+xy=x	$\frac{d y}{d x} + x y = x$
71305	Solve the Differential Equation	(dy)/(dx)-y=x	$\frac{d y}{d x} - y = x$
71306	Solve the Differential Equation	3y^2(dy)/(dx)=4x	$3 y^{2} \frac{d y}{d x} = 4 x$
71307	Solve the Differential Equation	(dy)/(dx)=(x^3)/y	$\frac{d y}{d x} = \frac{x^{3}}{y}$
71308	Solve the Differential Equation	y''''=1+x+y+xy	$y'' = 1 + x + y + x y$
71309	Solve the Differential Equation	(dy)/(dx)=(xy+y^2)/(x^2)	$\frac{d y}{d x} = \frac{x y + y^{2}}{x^{2}}$
71310	Solve the Differential Equation	(2y^2+3x)dx+2x(yd)y=0	$(2 y^{2} + 3 x) d x + 2 x yd y = 0$
71311	Solve the Differential Equation	(dy)/(dx)=6-3x^2	$\frac{d y}{d x} = 6 - 3 x^{2}$
71312	Solve the Differential Equation	(dy)/(dx)=4cos(6x)	$\frac{d y}{d x} = 4 \cos (6 x)$
71313	Solve the Differential Equation	xdy-(yd)x=2x^3dx	$x d y - yd x = 2 x^{3} d x$
71314	Solve the Differential Equation	2x(yd)x+(1+x^2)dy=0	$2 x yd x + (1 + x^{2}) d y = 0$
71315	Solve the Differential Equation	ydx+xdy=0	$yd x + x d y = 0$
71316	Solve the Differential Equation	(dy)/(dx)=4x	$\frac{d y}{d x} = 4 x$
71317	Solve the Differential Equation	(3x^2y+2xy+y^3)dx+(x^2+y^2)dy=0	$(3 x^{2} y + 2 x y + y^{3}) d x + (x^{2} + y^{2}) d y = 0$
71318	Solve the Differential Equation	(d^2y)/(dx^2)+4y=0	$\frac{d^{2} y}{d x^{2}} + 4 y = 0$
71319	Solve the Differential Equation	(dy)/(dx)=8xy	$\frac{d y}{d x} = 8 x y$
71320	Solve the Differential Equation	3(yd)x-(2x+1)dy=0	$3 yd x - (2 x + 1) d y = 0$
71321	Solve the Differential Equation	(16xy-3x^2)dx+(8x^2+2y)dy=0	$(16 x y - 3 x^{2}) d x + (8 x^{2} + 2 y) d y = 0$
71322	Solve the Differential Equation	(x+y/x)dx-dy=0	$(x + \frac{y}{x}) d x - d y = 0$
71323	Solve the Differential Equation	(dy)/(dx)=(y^2+2xy)/(x^2)	$\frac{d y}{d x} = \frac{y^{2} + 2 x y}{x^{2}}$
71324	Solve the Differential Equation	(dy)/(dx)=x+1	$\frac{d y}{d x} = x + 1$
71325	Solve the Differential Equation	5(dy)/(dx)-15xy-3x=0	$5 \frac{d y}{d x} - 15 x y - 3 x = 0$
71326	Solve the Differential Equation	(dy)/(dx)=(x-e^(-x))/(y+e^y)	$\frac{d y}{d x} = \frac{x - e^{- x}}{y + e^{y}}$
71327	Solve the Differential Equation	dx-x^2dy=0	$d x - x^{2} d y = 0$
71328	Solve the Differential Equation	(dy)/(dx)=-2xy^2	$\frac{d y}{d x} = - 2 x y^{2}$
71329	Solve the Differential Equation	y''''=2y-4x	$y'' = 2 y - 4 x$
71330	Solve the Differential Equation	(dy)/(dx)+2xy=8x	$\frac{d y}{d x} + 2 x y = 8 x$
71331	Solve the Differential Equation	y''''+y=sec(x)^2	$y'' + y = \sec^{2} (x)$
71332	Solve the Differential Equation	y''''-y=5.2	$y'' - y = 5.2$
71333	Solve the Differential Equation	xdx-y^3dy=0	$x d x - y^{3} d y = 0$
71334	Solve the Differential Equation	yp(dp)/(dy)+p^3=0	$y p \frac{d p}{d y} + p^{3} = 0$
71335	Solve the Differential Equation	y''''-2y=0	$y'' - 2 y = 0$
71336	Solve the Differential Equation	xy''''=2y	$x y'' = 2 y$
71337	Solve the Differential Equation	(dy)/(dx)=4x+(4x)/( square root of 16-x^2)	$\frac{d y}{d x} = 4 x + \frac{4 x}{\sqrt{16 - x^{2}}}$
71338	Solve the Differential Equation	(dy)/(dx)=1+y^2	$\frac{d y}{d x} = 1 + y^{2}$
71339	Solve the Differential Equation	(e^x+e^(-x))(dy)/(dx)=y^2	$(e^{x} + e^{- x}) \frac{d y}{d x} = y^{2}$
71340	Solve the Differential Equation	2x^2dx+y^2dy=0	$2 x^{2} d x + y^{2} d y = 0$
71341	Solve the Differential Equation	(dy)/(dx)=8x(y^2+1)	$\frac{d y}{d x} = 8 x (y^{2} + 1)$
71342	Solve the Differential Equation	x(dy)/(dx)=2xe^x-y+6x^2	$x \frac{d y}{d x} = 2 x e^{x} - y + 6 x^{2}$
71343	Solve the Differential Equation	y''''=2xy-x	$y'' = 2 x y - x$
71344	Solve the Differential Equation	(dy)/(dx)=6-y	$\frac{d y}{d x} = 6 - y$
71345	Solve the Differential Equation	(dy)/(dx)=cos(x)	$\frac{d y}{d x} = \cos (x)$
71346	Solve the Differential Equation	ydx+(3x-xy+2)dy=0	$yd x + (3 x - x y + 2) d y = 0$
71347	Solve the Differential Equation	xy''''-2y=2	$x y'' - 2 y = 2$
71348	Solve the Differential Equation	(dy)/(dx)=x-2y	$\frac{d y}{d x} = x - 2 y$
71349	Solve the Differential Equation	y''''+y=e^x	$y'' + y = e^{x}$
71350	Solve the Differential Equation	(dy)/(dx)-y/x=2x	$\frac{d y}{d x} - \frac{y}{x} = 2 x$
71351	Solve the Differential Equation	(dy)/(dx)=2y+3	$\frac{d y}{d x} = 2 y + 3$
71352	Solve the Differential Equation	(x^4+2y)dx-xdy=0	$(x^{4} + 2 y) d x - x d y = 0$
71353	Solve the Differential Equation	(dy)/(dx)+y=0	$\frac{d y}{d x} + y = 0$
71354	Solve the Differential Equation	(1+x)(dy)/(dx)=-3y	$(1 + x) \frac{d y}{d x} = - 3 y$
71355	Solve the Differential Equation	y''''''''-4y''''+5y=0	$y'''' - 4 y'' + 5 y = 0$
71356	Solve the Differential Equation	y''''=e^(x-y)	$y'' = e^{x - y}$
71357	Solve the Differential Equation	y''''''''+25y=0	$y'''' + 25 y = 0$
71358	Solve the Differential Equation	(dy)/(dx)=(3x^2+y^2)/(2xy)	$\frac{d y}{d x} = \frac{3 x^{2} + y^{2}}{2 x y}$
71359	Solve the Differential Equation	x^2(dy)/(dx)+y^2=xy	$x^{2} \frac{d y}{d x} + y^{2} = x y$
71360	Solve the Differential Equation	ydx-xdy=0	$yd x - x d y = 0$
71361	Solve the Differential Equation	x(dy)/(dx)+2y=x^-3	$x \frac{d y}{d x} + 2 y = x^{- 3}$
71362	Solve the Differential Equation	(x^2+1)(dy)/(dx)=xy	$(x^{2} + 1) \frac{d y}{d x} = x y$
71363	Solve the Differential Equation	(dP)/(dt)=4 square root of Pt	$\frac{d P}{d t} = 4 \sqrt{P t}$
71364	Solve the Differential Equation	(dy)/(dx)=5e^(x-y)	$\frac{d y}{d x} = 5 e^{x - y}$
71365	Solve the Differential Equation	(x^2+y^2)dx+2x(yd)y=0	$(x^{2} + y^{2}) d x + 2 x yd y = 0$
71366	Solve the Differential Equation	6y^2dx-x(2x^3+y)dy=0	$6 y^{2} d x - x (2 x^{3} + y) d y = 0$
71367	Solve the Differential Equation	2y-y''''=0	$2 y - y'' = 0$
71368	Solve the Differential Equation	(y-x+xycot(x))dx+xdy=0	$(y - x + x y \cot (x)) d x + x d y = 0$
71369	Solve the Differential Equation	(dy)/(dx)=sin(x)	$\frac{d y}{d x} = \sin (x)$
71370	Solve the Differential Equation	(4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0	$(4 x^{3} y^{3} - 2 x y) d x + (3 x^{4} y^{2} - x^{2}) d y = 0$
71371	Solve the Differential Equation	(dy)/(dx)=1+6xe^(x-y)	$\frac{d y}{d x} = 1 + 6 x e^{x - y}$
71372	Solve the Differential Equation	xy''''=y	$x y'' = y$
71373	Solve the Differential Equation	(dy)/(dx)-y=e^(2x)	$\frac{d y}{d x} - y = e^{2 x}$
71374	Solve the Differential Equation	y''''-x/(x^2+1)y=2x(x^2+1)	$y'' - \frac{x}{x^{2} + 1} y = 2 x (x^{2} + 1)$
71375	Solve the Differential Equation	(dy)/(dx)=(y^2-1)/x	$\frac{d y}{d x} = \frac{y^{2} - 1}{x}$
71376	Solve the Differential Equation	y''''+xy=xy^2	$y'' + x y = x y^{2}$
71377	Solve the Differential Equation	x(dy)/(dx)-2y=x^3cos(4x)	$x \frac{d y}{d x} - 2 y = x^{3} \cos (4 x)$
71378	Solve the Differential Equation	(dy)/(dx)=e^(y-x)	$\frac{d y}{d x} = e^{y - x}$
71379	Solve the Differential Equation	(dy)/(dx)=1-y	$\frac{d y}{d x} = 1 - y$
71380	Solve the Differential Equation	(dy)/(dx)=-1/(x^2)	$\frac{d y}{d x} = - \frac{1}{x^{2}}$
71381	Solve the Differential Equation	(dy)/(dx)=e^(2x)	$\frac{d y}{d x} = e^{2 x}$
71382	Solve the Differential Equation	(dy)/(dx)=1/(cos(y))	$\frac{d y}{d x} = \frac{1}{\cos (y)}$
71383	Solve the Differential Equation	(dy)/(dt)=-1/2y	$\frac{d y}{d t} = - \frac{1}{2} y$
71384	Solve the Differential Equation	(dy)/(dx)=(x^2)/(1+y^2)	$\frac{d y}{d x} = \frac{x^{2}}{1 + y^{2}}$
71385	Solve the Differential Equation	x(dy)/(dx)+(3x+1)y=e^(-3x)	$x \frac{d y}{d x} + (3 x + 1) y = e^{- 3 x}$
71386	Solve the Differential Equation	x(yd)x-(x+2y)*2dy=0	$x yd x - (x + 2 y) \cdot 2 d y = 0$
71387	Solve the Differential Equation	yy''''-xy^2+x=0	$y y'' - x y^{2} + x = 0$
71388	Solve the Differential Equation	2(yd)x+(x-x^3y^3)dy=0	$2 yd x + (x - x^{3} y^{3}) d y = 0$
71389	Solve the Differential Equation	(dy)/(dx)+y=e^(-x)	$\frac{d y}{d x} + y = e^{- x}$
71390	Solve the Differential Equation	xy^2dx+e^xdy=0	$x y^{2} d x + e^{x} d y = 0$
71391	Solve the Differential Equation	3y^2(dy)/(dx)+x^-1y^3=x^4	$3 y^{2} \frac{d y}{d x} + x^{- 1} y^{3} = x^{4}$
71392	Solve the Differential Equation	(dy)/(dx)=y-x	$\frac{d y}{d x} = y - x$
71393	Solve the Differential Equation	(dx)/(dy)+3/yx=2y	$\frac{d x}{d y} + \frac{3}{y} x = 2 y$
71394	Solve the Differential Equation	x(dy)/(dx)-y=2x^2y	$x \frac{d y}{d x} - y = 2 x^{2} y$
71395	Solve the Differential Equation	y''''=x^2y	$y'' = x^{2} y$
71396	Solve the Differential Equation	(dy)/(dx)=4cos(x-1) , y(1)=6	$\frac{d y}{d x} = 4 \cos (x - 1)$ , $y (1) = 6$
71397	Solve the Differential Equation	(dy)/(dx)+3y=0	$\frac{d y}{d x} + 3 y = 0$
71398	Solve the Differential Equation	(dy)/(dx)=2x+1	$\frac{d y}{d x} = 2 x + 1$
71399	Solve the Differential Equation	(dy)/(dx)=(x-5)/(y^2)	$\frac{d y}{d x} = \frac{x - 5}{y^{2}}$
71400	Solve the Differential Equation	(dy)/(dt)=2y	$\frac{d y}{d t} = 2 y$