Question #350870

Find the general solution of the given differential equation.

y' + 3x2y = x2

1
Expert's answer
2022-06-15T18:01:46-0400

Solution

From given differential equation

y'  = x2(1 – 3y)  => dy/(1 – 3y) = x2dx  => ∫dy/(1 – 3y) = ∫x2dx  =>  -ln|1 – 3y|/3 = x3/3 + C  =>  

13y=Dex31-3y=De^{-x^3}   =>  y=13[1Dex3]y=\frac{1}{3}\left[1-De^{-x^3}\right]

C and D are arbitrary constants.  

Answer

y=13[1Dex3]y=\frac{1}{3}\left[1-De^{-x^3}\right]



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