What is the solution for (dy)/(dx)+3x^2y=x ?

The solution for (dy)/(dx)+3x^2y=x is y=-(\Gamma(1/(3/2),-(x^2)^{3/2}))/(3e^{x^3)}+(c_{1})/(e^{x^3)}

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(dy)/(dx)+3x^2y=x

\frac{d y}{d x} + 3 x^{2} y = x

y = - \frac{Γ ( \frac{1}{\frac{3}{2}} , - ( x ^{2} ) ^{\frac{3}{2}} )}{3 e ^{x^{3}}} + \frac{c _{1}}{e ^{x^{3}}}

Solution steps

\frac{d y}{d x} + 3 x^{2} y = x

Solve linear ODE:

y = - \frac{Γ ( \frac{1}{\frac{3}{2}} , - ( x ^{2} ) ^{\frac{3}{2}} )}{3 e ^{x^{3}}} + \frac{c _{1}}{e ^{x^{3}}}

y = - \frac{Γ ( \frac{1}{\frac{3}{2}} , - ( x ^{2} ) ^{\frac{3}{2}} )}{3 e ^{x^{3}}} + \frac{c _{1}}{e ^{x^{3}}}

What is the solution for (dy)/(dx)+3x^2y=x ?
The solution for (dy)/(dx)+3x^2y=x is y=-(\Gamma(1/(3/2),-(x^2)^{3/2}))/(3e^{x^3)}+(c_{1})/(e^{x^3)}