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Popular >

y^'=x^2+2y

Solution

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

Solution

y = - \frac{x ^{2}}{2} - \frac{2 x + 1}{4} + c_{1} e^{2 x}

Solution steps

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

Solve linear ODE:

y = - \frac{x ^{2}}{2} - \frac{2 x + 1}{4} + c_{1} e^{2 x}

y = - \frac{x ^{2}}{2} - \frac{2 x + 1}{4} + c_{1} e^{2 x}

Popular Examples

integral of (1-tanh^3(3x))/(tanh(3x))

\int \frac{1 - tanh ^{3} ( 3 x )}{tanh ( 3 x )} d x

integral of (4x^3)/3

\int \frac{4 x ^{3}}{3} d x

0.5y^{''}+10y^'+100y=150

0.5 y^{^{''}} + 10 y^{^{'}} + 100 y = 150

limit as x approaches 1 of (x)^{1/(1-x)}

x \to 1 lim ((x)^{\frac{1}{1 - x}})

derivative of-(2x/y)

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

Frequently Asked Questions (FAQ)

What is the solution for y^'=x^2+2y ?
The solution for y^'=x^2+2y is y=-(x^2)/2-(2x+1)/4+c_{1}e^{2x}