Question #350870

Find the general solution of the given differential equation.

*y'* + 3*x*^{2}*y* = *x*^{2}

Expert's answer

**Solution**

From given differential equation

*y' = x*^{2}*(1 – 3y) => dy/(1 – 3y) = x*^{2}*dx => ∫dy/(1 – 3y) = ∫x*^{2}*dx => -ln|1 – 3y|/3 = x*^{3}*/3 + C => *

"1-3y=De^{-x^3}" * => * * *"y=\\frac{1}{3}\\left[1-De^{-x^3}\\right]"

C and D are arbitrary constants.

**Answer**

"y=\\frac{1}{3}\\left[1-De^{-x^3}\\right]"

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