Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72301	Solve the Differential Equation	y''''''''+2y=0	$y'''' + 2 y = 0$
72302	Solve the Differential Equation	xy(dy)/(dx)=(x^2+1)/(y+1)	$x y \frac{d y}{d x} = \frac{x^{2} + 1}{y + 1}$
72303	Solve the Differential Equation	(2x+4)dx+(3y-1)dy=0	$(2 x + 4) d x + (3 y - 1) d y = 0$
72304	Solve the Differential Equation	(dy)/(dx)=8x^7 square root of y-1	$\frac{d y}{d x} = 8 x^{7} \sqrt{y - 1}$
72305	Solve the Differential Equation	(dy)/(dx)+4y=0	$\frac{d y}{d x} + 4 y = 0$
72306	Solve the Differential Equation	x(dy)/(dx)+2y=x^2	$x \frac{d y}{d x} + 2 y = x^{2}$
72307	Solve the Differential Equation	-(y^2)/(t^2)dt+(2y)/tdy=0	$- \frac{y^{2}}{t^{2}} d t + \frac{2 y}{t} d y = 0$
72308	Solve the Differential Equation	(2xy+y^2)dx-2x^2dy=0	$(2 x y + y^{2}) d x - 2 x^{2} d y = 0$
72309	Solve the Differential Equation	y''''=2	$y'' = 2$
72310	Solve the Differential Equation	y''''=(x^2-4)(3y+2)	$y'' = (x^{2} - 4) (3 y + 2)$
72311	Solve the Differential Equation	xy''''+2y=7x^2	$x y'' + 2 y = 7 x^{2}$
72312	Solve the Differential Equation	xy(dy)/(dx)=x^2+y^2	$x y \frac{d y}{d x} = x^{2} + y^{2}$
72313	Solve the Differential Equation	(dy)/(dx)=-(x^2)/(y^2)	$\frac{d y}{d x} = - \frac{x^{2}}{y^{2}}$
72314	Solve the Differential Equation	(dy)/(dx)-(2y)/x=x^3	$\frac{d y}{d x} - \frac{2 y}{x} = x^{3}$
72315	Solve the Differential Equation	y''''=e^(y/x)+y/x	$y'' = e^{\frac{y}{x}} + \frac{y}{x}$
72316	Solve the Differential Equation	(x-3y+2)dx+3(x+3y-4)dy=0	$(x - 3 y + 2) d x + 3 (x + 3 y - 4) d y = 0$
72317	Solve the Differential Equation	(dy)/(dx)=(32x)/(e^y)	$\frac{d y}{d x} = \frac{32 x}{e^{y}}$
72318	Solve the Differential Equation	(2+x)y''''=3y	$(2 + x) y'' = 3 y$
72319	Solve the Differential Equation	x(dy)/(dx)-y=x^3	$x \frac{d y}{d x} - y = x^{3}$
72320	Solve the Differential Equation	(dy)/(dx)=1+e^(y-x+5)	$\frac{d y}{d x} = 1 + e^{y - x + 5}$
72321	Solve the Differential Equation	y''''''''+2y''''+5y=0	$y'''' + 2 y'' + 5 y = 0$
72322	Solve the Differential Equation	(dy)/(dx)=4x+1	$\frac{d y}{d x} = 4 x + 1$
72323	Solve the Differential Equation	(dy)/(dx)+5y=10	$\frac{d y}{d x} + 5 y = 10$
72324	Solve the Differential Equation	y''''=1/( square root of 1-x^2)	$y'' = \frac{1}{\sqrt{1 - x^{2}}}$
72325	Solve the Differential Equation	(x^2+y^2)dx+2x(yd)y=0	$(x^{2} + y^{2}) d x + 2 x yd y = 0$
72326	Solve the Differential Equation	(dy)/(dx)+x/y=0	$\frac{d y}{d x} + \frac{x}{y} = 0$
72327	Solve the Differential Equation	(dy)/(dx)=(x^4)/y	$\frac{d y}{d x} = \frac{x^{4}}{y}$
72328	Solve the Differential Equation	x(yd)x-(x^2+1)dy=0	$x yd x - (x^{2} + 1) d y = 0$
72329	Solve the Differential Equation	y''''''''''''+3y''''''''-4y''''-12y=0	$y'''''' + 3 y'''' - 4 y'' - 12 y = 0$
72330	Solve the Differential Equation	(y+x^3y^3)dx+xdy=0	$(y + x^{3} y^{3}) d x + x d y = 0$
72331	Solve the Differential Equation	(dy)/(dx)+1/xy=xy^2	$\frac{d y}{d x} + \frac{1}{x} y = x y^{2}$
72332	Solve the Differential Equation	(dy)/(dx)=-10x+3x^2	$\frac{d y}{d x} = - 10 x + 3 x^{2}$
72333	Solve the Differential Equation	xy''''-y=x^3	$x y'' - y = x^{3}$
72334	Solve the Differential Equation	y''''''''-4y''''+4y=e^t	$y'''' - 4 y'' + 4 y = e^{t}$
72335	Solve the Differential Equation	(dy)/(dx)=(y+5)(x+2)	$\frac{d y}{d x} = (y + 5) (x + 2)$
72336	Solve the Differential Equation	(y^2-x^2)dy=2x(yd)x	$(y^{2} - x^{2}) d y = 2 x yd x$
72337	Solve the Differential Equation	y(x+1)+(dy)/(dx)=0	$y (x + 1) + \frac{d y}{d x} = 0$
72338	Solve the Differential Equation	(dy)/(dx)=(e^(2x-y))/(e^(x+y))	$\frac{d y}{d x} = \frac{e^{2 x - y}}{e^{x + y}}$
72339	Solve the Differential Equation	(dy)/(dx)=(y-1)(y+1)	$\frac{d y}{d x} = (y - 1) (y + 1)$
72340	Solve the Differential Equation	(dy)/(dx)=1/( square root of x)	$\frac{d y}{d x} = \frac{1}{\sqrt{x}}$
72341	Solve the Differential Equation	(dy)/(dx)=x^2e^(-4x)-4y	$\frac{d y}{d x} = x^{2} e^{- 4 x} - 4 y$
72342	Solve the Differential Equation	(dy)/(dx)=sec(y)tan(x)	$\frac{d y}{d x} = \sec (y) \tan (x)$
72343	Solve the Differential Equation	(cos(x)cos(y)-cot(x))dx-sin(x)sin(ydy)=0	$(\cos (x) \cos (y) - \cot (x)) d x - \sin (x) \sin (yd y) = 0$
72344	Solve the Differential Equation	(dy)/(dx)=x+xy	$\frac{d y}{d x} = x + x y$
72345	Solve the Differential Equation	3x(dy)/(dx)+2y=xy^4	$3 x \frac{d y}{d x} + 2 y = x y^{4}$
72346	Solve the Differential Equation	(dy)/(dx)+(x^2+1)y=sin(x)	$\frac{d y}{d x} + (x^{2} + 1) y = \sin (x)$
72347	Solve the Differential Equation	cos(x)(dy)/(dx)+ysin(x)=1	$\cos (x) \frac{d y}{d x} + y \sin (x) = 1$
72348	Solve the Differential Equation	(dr)/(dtheta)=pi	$\frac{d r}{d θ} = π$
72349	Solve the Differential Equation	x^2(dy)/(dx)-x^3+xy=0	$x^{2} \frac{d y}{d x} - x^{3} + x y = 0$
72350	Solve the Differential Equation	(dy)/(dx)=-11y	$\frac{d y}{d x} = - 11 y$
72351	Solve the Differential Equation	f(x)=2x^3+5x	$f (x) = 2 x^{3} + 5 x$
72352	Solve the Differential Equation	x(dy)/(dx)-y=x^2	$x \frac{d y}{d x} - y = x^{2}$
72353	Solve the Differential Equation	(dy)/(dx)=(y-1)/(x+3)	$\frac{d y}{d x} = \frac{y - 1}{x + 3}$
72354	Solve the Differential Equation	x^2+5y(dy)/(dx)=0	$x^{2} + 5 y \frac{d y}{d x} = 0$
72355	Solve the Differential Equation	(ds)/(dt)=12t(3t^2-1)^3	$\frac{d s}{d t} = 12 t {(3 t^{2} - 1)}^{3}$
72356	Solve the Differential Equation	(dy)/(dx)+y=4e^x	$\frac{d y}{d x} + y = 4 e^{x}$
72357	Solve the Differential Equation	y''''+3x^2y=4x^2y^2	$y'' + 3 x^{2} y = 4 x^{2} y^{2}$
72358	Solve the Differential Equation	(dy)/(dx)=1+y	$\frac{d y}{d x} = 1 + y$
72359	Solve the Differential Equation	(dy)/(dx)=(y^2)/(x^2)	$\frac{d y}{d x} = \frac{y^{2}}{x^{2}}$
72360	Solve the Differential Equation	(y+x^4)dx-xdy=0	$(y + x^{4}) d x - x d y = 0$
72361	Solve the Differential Equation	(dy)/(dx)=(x+xy^2)/(4y)	$\frac{d y}{d x} = \frac{x + x y^{2}}{4 y}$
72362	Solve the Differential Equation	(dy)/(dx)=xy^2-4x	$\frac{d y}{d x} = x y^{2} - 4 x$
72363	Solve the Differential Equation	(6x^2y^2-4y^4)dx+(2x^3y-4xy^3)dy=0	$(6 x^{2} y^{2} - 4 y^{4}) d x + (2 x^{3} y - 4 x y^{3}) d y = 0$
72364	Solve the Differential Equation	y''''=(1-2x)^2	$y'' = {(1 - 2 x)}^{2}$
72365	Solve the Differential Equation	(dr)/(dtheta)=-picos(pitheta) , r(2)=2	$\frac{d r}{d θ} = - π \cos (π θ)$ , $r (2) = 2$
72366	Solve the Differential Equation	(dy)/(dx)=y(x^2+1)	$\frac{d y}{d x} = y (x^{2} + 1)$
72367	Solve the Differential Equation	e^(y''''+y)=x	$e^{y'' + y} = x$
72368	Solve the Differential Equation	y''''=8x+xy	$y'' = 8 x + x y$
72369	Solve the Differential Equation	(dy)/(dx)=e^(0.01x)	$\frac{d y}{d x} = e^{0.01 x}$
72370	Solve the Differential Equation	(dy)/(dx)=(x+9)/(y-9)	$\frac{d y}{d x} = \frac{x + 9}{y - 9}$
72371	Solve the Differential Equation	y''''''''+3y=0	$y'''' + 3 y = 0$
72372	Solve the Differential Equation	xy''''+(1+x)y=e^(-x)sin(2x)	$x y'' + (1 + x) y = e^{- x} \sin (2 x)$
72373	Solve the Differential Equation	y''''''''''''-3y''''''''+3y''''-y=0	$y'''''' - 3 y'''' + 3 y'' - y = 0$
72374	Solve the Differential Equation	(2x+y^2)dx+2x(yd)y=0	$(2 x + y^{2}) d x + 2 x yd y = 0$
72375	Solve the Differential Equation	(x+2y-1)dx+(2x+4y-3)dy=0	$(x + 2 y - 1) d x + (2 x + 4 y - 3) d y = 0$
72376	Solve the Differential Equation	(1+y)dx=(x-1)dy	$(1 + y) d x = (x - 1) d y$
72377	Solve the Differential Equation	(dy)/(dx)=(3x square root of 1+y^2)/y	$\frac{d y}{d x} = \frac{3 x \sqrt{1 + y^{2}}}{y}$
72378	Solve the Differential Equation	y''''=2y+x	$y'' = 2 y + x$
72379	Solve the Differential Equation	(dx)/(dy)+0.035x=0.3	$\frac{d x}{d y} + 0.035 x = 0.3$
72380	Solve the Differential Equation	(y-xy)dx+xdy=0	$(y - x y) d x + x d y = 0$
72381	Solve the Differential Equation	(dy)/(dx)=e^(3x)+2e^(-x)	$\frac{d y}{d x} = e^{3 x} + 2 e^{- x}$
72382	Solve the Differential Equation	(2xy+x)dx+(x^2+y)dy=0	$(2 x y + x) d x + (x^{2} + y) d y = 0$
72383	Solve the Differential Equation	(2xy^2+x/(y^2))dx+4x^2(yd)y=0	$(2 x y^{2} + \frac{x}{y^{2}}) d x + 4 x^{2} yd y = 0$
72384	Solve the Differential Equation	(dy)/(dx)=2x+y/x-x	$\frac{d y}{d x} = 2 x + \frac{y}{x} - x$
72385	Solve the Differential Equation	(dy)/(dx)=4	$\frac{d y}{d x} = 4$
72386	Solve the Differential Equation	(e^(2y)-y)cos(x)(dy)/(dx)=e^ysin(2x)	$(e^{2 y} - y) \cos (x) \frac{d y}{d x} = e^{y} \sin (2 x)$
72387	Solve the Differential Equation	xy^4dx+(y^2+2)e^(-3x)dy=0	$x y^{4} d x + (y^{2} + 2) e^{- 3 x} d y = 0$
72388	Solve the Differential Equation	(x^2+1)y''''=xy	$(x^{2} + 1) y'' = x y$
72389	Solve the Differential Equation	(dy)/(dx)+2y=e^x	$\frac{d y}{d x} + 2 y = e^{x}$
72390	Solve the Differential Equation	(dy)/(dx)+2xy=2x	$\frac{d y}{d x} + 2 x y = 2 x$
72391	Solve the Differential Equation	y^2dt+t^2dy=0	$y^{2} d t + t^{2} d y = 0$
72392	Solve the Differential Equation	square root of x(dy)/(dx)=e^(y+ square root of x)	$\sqrt{x} \frac{d y}{d x} = e^{y + \sqrt{x}}$
72393	Solve the Differential Equation	(6x-3y+2)dx-(2x-y-1)dy=0	$(6 x - 3 y + 2) d x - (2 x - y - 1) d y = 0$
72394	Solve the Differential Equation	y((dx)/(dy))+2x=5y^3	$y (\frac{d x}{d y}) + 2 x = 5 y^{3}$
72395	Solve the Differential Equation	(dy)/(dx)=tan(x)	$\frac{d y}{d x} = \tan (x)$
72396	Solve the Differential Equation	(ds)/(dt)=12t(3t^2-1)^3 , s(1)=5	$\frac{d s}{d t} = 12 t {(3 t^{2} - 1)}^{3}$ , $s (1) = 5$
72397	Solve the Differential Equation	(dy)/(dx)=(x+2)/(y^2)	$\frac{d y}{d x} = \frac{x + 2}{y^{2}}$
72398	Solve the Differential Equation	2(dy)/(dx)=(y(x+1))/x	$2 \frac{d y}{d x} = \frac{y (x + 1)}{x}$
72399	Solve the Differential Equation	(dy)/(dx)=(6x)/(e^y)	$\frac{d y}{d x} = \frac{6 x}{e^{y}}$
72400	Solve the Differential Equation	(dy)/(dx)=ysec(x)^2	$\frac{d y}{d x} = y \sec^{2} (x)$