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Popular >

xy^'=y+x^2e^{2x}

Solution

x y^{^{'}} = y + x^{2} e^{2 x}

Solution

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

Solution steps

x y^{'} (x) = y + x^{2} e^{2 x}

Solve linear ODE:

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

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

Popular Examples

integral from 0 to pi of (sin^2(x))

\int_{0}^{π} (sin^{2} (x)) d x

limit as x approaches 0 of (cos(10x)-1)/(x^2)

x \to 0 lim (\frac{cos ( 10 x ) - 1}{x ^{2}})

integral of (4x+1)^2e^{2x}

\int (4 x + 1)^{2} e^{2 x} d x

integral of cos(2/3 x)

\int cos (\frac{2}{3} x) d x

y^{''}+4y^'+3y=20te^{5t}

y^{^{''}} + 4 y^{^{'}} + 3 y = 20 t e^{5 t}

Frequently Asked Questions (FAQ)

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