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Popular >

xy^'=(x^2-1)y

Solution

x y^{^{'}} = (x^{2} - 1) y

Solution

y = \frac{e ^{\frac{x ^{2} + c _{1}}{2}}}{x}

Solution steps

x y^{'} (x) = (x^{2} - 1) y

Solve separable ODE:

y = \frac{e ^{\frac{x ^{2} + c _{1}}{2}}}{x}

y = \frac{e ^{\frac{x ^{2} + c _{1}}{2}}}{x}

Graph

Popular Examples

y^{^{'}} \cdot tan (x) = y

(dy)/(dx)=(3x-2)^3e^{2y},y=0,x=1

\frac{d y}{d x} = (3 x - 2)^{3} e^{2 y}, y = 0, x = 1

(dy)/(dt)y= 1/(2sqrt(81))*9

\frac{d y}{d t} y = \frac{1}{2 81} \cdot 9

(dy)/(dx)= y/((2x))

\frac{d y}{d x} = \frac{y}{( 2 x )}

y^'+y/4 =3,y(-3)=0

y^{^{'}} + \frac{y}{4} = 3, y (- 3) = 0

Frequently Asked Questions (FAQ)

What is the solution for xy^'=(x^2-1)y ?
The solution for xy^'=(x^2-1)y is y=(e^{(x^2+c_{1})/2})/(x)