What is the solution for xy^'=(1-x)y+x^2+x^3 ?

The solution for xy^'=(1-x)y+x^2+x^3 is y=x^2+(c_{1}x)/(e^{x+c_{1)}}

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xy^'=(1-x)y+x^2+x^3

x y^{^{'}} = (1 - x) y + x^{2} + x^{3}

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

Solution steps

x y^{'} (x) = (1 - x) y + x^{2} + x^{3}

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} = cos^{2} (x)

\int - \frac{1}{10 - x} d x

\int cos^{3} (x) (sin (x)) d x

y = x^{2} - 8, y = 1

y = 5 e^{5 t + 1}

What is the solution for xy^'=(1-x)y+x^2+x^3 ?
The solution for xy^'=(1-x)y+x^2+x^3 is y=x^2+(c_{1}x)/(e^{x+c_{1)}}