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Popular >

(df)/(dx)-xf(x)=0

Solution

\frac{df}{d x} - x f (x) = 0

Solution

f (x) = e^{\frac{x ^{2}}{2} + c_{1}}

Solution steps

\frac{df}{d x} - x f = 0

Solve separable ODE:

f (x) = e^{\frac{x ^{2}}{2} + c_{1}}

f (x) = e^{\frac{x ^{2}}{2} + c_{1}}

Graph

Popular Examples

(2xy^4+2xy^2)dx+(x^2y^3+x^2y)dy=0

(2 x y^{4} + 2 x y^{2}) d x + (x^{2} y^{3} + x^{2} y) d y = 0

(1+y^2)dx=(y-sqrt(1+y^2))(1+x^2)^{3/2}dy

(1 + y^{2}) d x = (y - 1 + y^{2}) (1 + x^{2})^{\frac{3}{2}} d y

(dy)/(dt)=5+5y+t+ty,y(0)=3

\frac{d y}{d t} = 5 + 5 y + t + t y, y (0) = 3

(x^2+1)dy+xy^2dx=0

(x^{2} + 1) d y + x y^{2} d x = 0

x + y \frac{d y}{d x} = 0

Frequently Asked Questions (FAQ)

What is the solution for (df)/(dx)-xf(x)=0 ?
The solution for (df)/(dx)-xf(x)=0 is f(x)=e^{(x^2)/2+c_{1}}