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Popular >

y^'=y+xy

Solution

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

Solution

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

Solution steps

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

Solve separable ODE:

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

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

Popular Examples

sum from n=1 to infinity of (((3n-1))/((3n)))^{n^2}

n = 1 \sum \infty (\frac{( 3 n - 1 )}{( 3 n )})^{n^{2}}

tan(x)sin^2(y)dx+cos^2(x)cot(y)dy=0

tan (x) sin^{2} (y) d x + cos^{2} (x) cot (y) d y = 0

sum from n=0 to infinity of 1+1/(n^2)

n = 0 \sum \infty 1 + \frac{1}{n ^{2}}

y^{^{'}} = 32 x^{3} y^{3}

integral from-2 to 2 of x^2e^{x^3+8}

\int_{- 2}^{2} x^{2} e^{x^{3} + 8} d x

Frequently Asked Questions (FAQ)

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