Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
71201	Solve the Differential Equation	(x^2-9)(dy)/(dx)+xy=0	$(x^{2} - 9) \frac{d y}{d x} + x y = 0$
71202	Solve the Differential Equation	2x^3y''''=y(y^2+3x^2)	$2 x^{3} y'' = y (y^{2} + 3 x^{2})$
71203	Solve the Differential Equation	(dx)/(dt)-x=t+1	$\frac{d x}{d t} - x = t + 1$
71204	Solve the Differential Equation	(dy)/(dx)=y(2+sin(x))	$\frac{d y}{d x} = y (2 + \sin (x))$
71205	Solve the Differential Equation	xyy''''=1+y^2	$x y y'' = 1 + y^{2}$
71206	Solve the Differential Equation	(1+x^2)y''''=x^4y^4	$(1 + x^{2}) y'' = x^{4} y^{4}$
71207	Solve the Differential Equation	y''''''''-9y=0	$y'''' - 9 y = 0$
71208	Solve the Differential Equation	(1+x^2)(dy)/(dx)+xy=0	$(1 + x^{2}) \frac{d y}{d x} + x y = 0$
71209	Solve the Differential Equation	(dx)/(dy)+y^2x=x^2y^2	$\frac{d x}{d y} + y^{2} x = x^{2} y^{2}$
71210	Solve the Differential Equation	y''''+xy=6x square root of y	$y'' + x y = 6 x \sqrt{y}$
71211	Solve the Differential Equation	2(12)(18)+2(9)(dy)/(dt)=0	$2 (12) (18) + 2 (9) \frac{d y}{d t} = 0$
71212	Solve the Differential Equation	(dy)/(dx)=(3x^2)/(y^2)	$\frac{d y}{d x} = \frac{3 x^{2}}{y^{2}}$
71213	Solve the Differential Equation	x(dy)/(dx)=y	$x \frac{d y}{d x} = y$
71214	Solve the Differential Equation	(dy)/(dx)=8y	$\frac{d y}{d x} = 8 y$
71215	Solve the Differential Equation	(dy)/(dx)=6xy	$\frac{d y}{d x} = 6 x y$
71216	Solve the Differential Equation	(dy)/(dx)=5x-7	$\frac{d y}{d x} = 5 x - 7$
71217	Solve the Differential Equation	(2x-5y+2)dx+(1-6y-5x)dy=0	$(2 x - 5 y + 2) d x + (1 - 6 y - 5 x) d y = 0$
71218	Solve the Differential Equation	x^2(dy)/(dx)+xy=1	$x^{2} \frac{d y}{d x} + x y = 1$
71219	Solve the Differential Equation	x(dy)/(dx)+9y+6=6x^2+(dy)/(dx)+8y	$x \frac{d y}{d x} + 9 y + 6 = 6 x^{2} + \frac{d y}{d x} + 8 y$
71220	Solve the Differential Equation	x^2(dy)/(dx)+2xy=3x^2	$x^{2} \frac{d y}{d x} + 2 x y = 3 x^{2}$
71221	Solve the Differential Equation	y''''=5y	$y'' = 5 y$
71222	Solve the Differential Equation	y''''''''-y''''=0	$y'''' - y'' = 0$
71223	Solve the Differential Equation	y''''=x^2	$y'' = x^{2}$
71224	Solve the Differential Equation	(dy)/(dx)=5sin(10x)	$\frac{d y}{d x} = 5 \sin (10 x)$
71225	Solve the Differential Equation	(x^2-9)dy-x(yd)x=0	$(x^{2} - 9) d y - x yd x = 0$
71226	Solve the Differential Equation	(dy)/(dx)=5x-4	$\frac{d y}{d x} = 5 x - 4$
71227	Solve the Differential Equation	(dy)/(dx)=(y+1)/x	$\frac{d y}{d x} = \frac{y + 1}{x}$
71228	Solve the Differential Equation	y''''=2y	$y'' = 2 y$
71229	Solve the Differential Equation	y''''=(2y^4+x^4)/(xy^3)	$y'' = \frac{2 y^{4} + x^{4}}{x y^{3}}$
71230	Solve the Differential Equation	(dy)/(dx)=2x+3	$\frac{d y}{d x} = 2 x + 3$
71231	Solve the Differential Equation	(dy)/(dx)=xy^(1/2)	$\frac{d y}{d x} = x y^{\frac{1}{2}}$
71232	Solve the Differential Equation	(1+y^2+xy^2)dx+(x^2y+y+2xy)dy=0	$(1 + y^{2} + x y^{2}) d x + (x^{2} y + y + 2 x y) d y = 0$
71233	Solve the Differential Equation	(dy)/(dx)=(xy)/2	$\frac{d y}{d x} = \frac{x y}{2}$
71234	Solve the Differential Equation	y''''''''-10y''''+25y=30x+3	$y'''' - 10 y'' + 25 y = 30 x + 3$
71235	Solve the Differential Equation	(dy)/(dx)=4x-6	$\frac{d y}{d x} = 4 x - 6$
71236	Solve the Differential Equation	(dy)/(dx)=9y	$\frac{d y}{d x} = 9 y$
71237	Solve the Differential Equation	(dy)/(dx)=1/(sec(y)^2)	$\frac{d y}{d x} = \frac{1}{\sec^{2} (y)}$
71238	Solve the Differential Equation	(dy)/(dx)=1	$\frac{d y}{d x} = 1$
71239	Solve the Differential Equation	(dy)/(dx)=y/(2x)	$\frac{d y}{d x} = \frac{y}{2 x}$
71240	Solve the Differential Equation	(dy)/(dx)=(2x)/(y^2)	$\frac{d y}{d x} = \frac{2 x}{y^{2}}$
71241	Solve the Differential Equation	(dy)/(dx)=(x+y+1)^2	$\frac{d y}{d x} = {(x + y + 1)}^{2}$
71242	Solve the Differential Equation	xdx+ydy=0	$x d x + yd y = 0$
71243	Solve the Differential Equation	(dy)/(dx)-y=e^(3x)	$\frac{d y}{d x} - y = e^{3 x}$
71244	Solve the Differential Equation	(dy)/(dx)=6y^2x	$\frac{d y}{d x} = 6 y^{2} x$
71245	Solve the Differential Equation	(dy)/(dx)=ycos(x)	$\frac{d y}{d x} = y \cos (x)$
71246	Solve the Differential Equation	4y''''+y''''=0	$4 y'' + y'' = 0$
71247	Solve the Differential Equation	(dy)/(dx)=2y^2	$\frac{d y}{d x} = 2 y^{2}$
71248	Solve the Differential Equation	(x-y)dx+xdy=0	$(x - y) d x + x d y = 0$
71249	Solve the Differential Equation	3x^2y^2dx+(2x^3y+4y^3)dy=0	$3 x^{2} y^{2} d x + (2 x^{3} y + 4 y^{3}) d y = 0$
71250	Solve the Differential Equation	(2x+3)y''''=y+(2x+3)^(1/2)	$(2 x + 3) y'' = y + {(2 x + 3)}^{\frac{1}{2}}$
71251	Solve the Differential Equation	(dy)/(dx)=y/2	$\frac{d y}{d x} = \frac{y}{2}$
71252	Solve the Differential Equation	(dy)/(dx)=(1-x-y)/(x+y)	$\frac{d y}{d x} = \frac{1 - x - y}{x + y}$
71253	Solve the Differential Equation	y''''+(4/(x+2))y=6/((x+2)^2)	$y'' + (\frac{4}{x + 2}) y = \frac{6}{{(x + 2)}^{2}}$
71254	Solve the Differential Equation	(dy)/(dt)=k square root of t	$\frac{d y}{d t} = k \sqrt{t}$
71255	Solve the Differential Equation	(y+2xy^3)dx+(1+3x^2y^2+x)dy=0	$(y + 2 x y^{3}) d x + (1 + 3 x^{2} y^{2} + x) d y = 0$
71256	Solve the Differential Equation	(dy)/(dx)=(1-x^2+y^2-x^2y^2)/(x^2)	$\frac{d y}{d x} = \frac{1 - x^{2} + y^{2} - x^{2} y^{2}}{x^{2}}$
71257	Solve the Differential Equation	y^2dx-x(yd)y=x^2(yd)y	$y^{2} d x - x yd y = x^{2} yd y$
71258	Solve the Differential Equation	y''''=ysec(x)	$y'' = y \sec (x)$
71259	Solve the Differential Equation	y''''=e^(2x+3)	$y'' = e^{2 x + 3}$
71260	Solve the Differential Equation	(6x+y^2)dx+y(2x-3y)dy=0	$(6 x + y^{2}) d x + y (2 x - 3 y) d y = 0$
71261	Solve the Differential Equation	(dy)/(dx)=3x^2e^(-y)	$\frac{d y}{d x} = 3 x^{2} e^{- y}$
71262	Solve the Differential Equation	(dy)/(dx)=x^2y^3	$\frac{d y}{d x} = x^{2} y^{3}$
71263	Solve the Differential Equation	5y^4(dy)/(dx)=6x	$5 y^{4} \frac{d y}{d x} = 6 x$
71264	Solve the Differential Equation	(dy)/(dx)=10xy	$\frac{d y}{d x} = 10 x y$
71265	Solve the Differential Equation	y''''=e^(3x)-x	$y'' = e^{3 x} - x$
71266	Solve the Differential Equation	(dy)/(dx)=(x^2+3y^2)/(2xy)	$\frac{d y}{d x} = \frac{x^{2} + 3 y^{2}}{2 x y}$
71267	Solve the Differential Equation	(dy)/(dx)=(x^3+y^3)/(xy^2)	$\frac{d y}{d x} = \frac{x^{3} + y^{3}}{x y^{2}}$
71268	Solve the Differential Equation	(2x+3y)dx+(3x-4y)dy=0	$(2 x + 3 y) d x + (3 x - 4 y) d y = 0$
71269	Solve the Differential Equation	(dy)/(dx)=tan(x)^2	$\frac{d y}{d x} = \tan^{2} (x)$
71270	Solve the Differential Equation	xy''''+y=0	$x y'' + y = 0$
71271	Solve the Differential Equation	(dy)/(dx)+5y=0	$\frac{d y}{d x} + 5 y = 0$
71272	Solve the Differential Equation	(dy)/(dx)=(5x)/y	$\frac{d y}{d x} = \frac{5 x}{y}$
71273	Solve the Differential Equation	(x^3+y^3)dx-3xy^2dy=0	$(x^{3} + y^{3}) d x - 3 x y^{2} d y = 0$
71274	Solve the Differential Equation	y''''''''+16y=0	$y'''' + 16 y = 0$
71275	Solve the Differential Equation	(dy)/(dx)-0.01y=0	$\frac{d y}{d x} - 0.01 y = 0$
71276	Solve the Differential Equation	x(dy)/(dx)+2y=4x^2	$x \frac{d y}{d x} + 2 y = 4 x^{2}$
71277	Solve the Differential Equation	(dy)/(dx)=x+4y-2	$\frac{d y}{d x} = x + 4 y - 2$
71278	Solve the Differential Equation	xy^2(dy)/(dx)=y^3-x^3	$x y^{2} \frac{d y}{d x} = y^{3} - x^{3}$
71279	Solve the Differential Equation	x(dy)/(dx)=6y	$x \frac{d y}{d x} = 6 y$
71280	Solve the Differential Equation	(dy)/(dx)=2xy^3	$\frac{d y}{d x} = 2 x y^{3}$
71281	Solve the Differential Equation	y''''-y=e^x	$y'' - y = e^{x}$
71282	Solve the Differential Equation	y''''+xe^y=0	$y'' + x e^{y} = 0$
71283	Solve the Differential Equation	5y^4(dy)/(dx)=4x	$5 y^{4} \frac{d y}{d x} = 4 x$
71284	Solve the Differential Equation	(dy)/(dx)=xe^y , y(0)=0	$\frac{d y}{d x} = x e^{y}$ , $y (0) = 0$
71285	Solve the Differential Equation	(dy)/(dx)-1/(e^y+2x)=0	$\frac{d y}{d x} - \frac{1}{e^{y} + 2 x} = 0$
71286	Solve the Differential Equation	(1+x)dy-(yd)x=0	$(1 + x) d y - yd x = 0$
71287	Solve the Differential Equation	(dy)/(dx)=x+3	$\frac{d y}{d x} = x + 3$
71288	Solve the Differential Equation	y''''''''+y''''+y=0	$y'''' + y'' + y = 0$
71289	Solve the Differential Equation	x(yd)x+(x^2-3y)dy=0	$x yd x + (x^{2} - 3 y) d y = 0$
71290	Solve the Differential Equation	x(dy)/(dx)+2y=3	$x \frac{d y}{d x} + 2 y = 3$
71291	Solve the Differential Equation	2(2xy+4y-3)dx+(x+2)^2dy=0	$2 (2 x y + 4 y - 3) d x + {(x + 2)}^{2} d y = 0$
71292	Solve the Differential Equation	(dy)/(dt)=81t^8	$\frac{d y}{d t} = 81 t^{8}$
71293	Solve the Differential Equation	(dp)/(dt)+2tp=p+4t-2	$\frac{d p}{d t} + 2 t p = p + 4 t - 2$
71294	Solve the Differential Equation	(dy)/(dx)+4xy=0	$\frac{d y}{d x} + 4 x y = 0$
71295	Solve the Differential Equation	y''''=(x^2+y^2)/(2xy)	$y'' = \frac{x^{2} + y^{2}}{2 x y}$
71296	Solve the Differential Equation	(dy)/(dx)=(x^2y^2)/(1+x)	$\frac{d y}{d x} = \frac{x^{2} y^{2}}{1 + x}$
71297	Solve the Differential Equation	(cos(2y)-3x^2y^2)dx+(cos(2y)-2xsin(2y)-2x^3y)dy=0	$(\cos (2 y) - 3 x^{2} y^{2}) d x + (\cos (2 y) - 2 x \sin (2 y) - 2 x^{3} y) d y = 0$
71298	Solve the Differential Equation	(dy)/(dx)=(2x)/(e^(2y))	$\frac{d y}{d x} = \frac{2 x}{e^{2 y}}$
71299	Solve the Differential Equation	(dy)/(dx)-2y=y^2	$\frac{d y}{d x} - 2 y = y^{2}$
71300	Solve the Differential Equation	(dy)/(dx)=sin(x+y)	$\frac{d y}{d x} = \sin (x + y)$