What is the solution for (1+x^5)y^'+5x^4y=13x^4,y(0)=2 ?

The solution for (1+x^5)y^'+5x^4y=13x^4,y(0)=2 is y=(13x^5)/(5(1+x^5))+2/(1+x^5)

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(1+x^5)y^'+5x^4y=13x^4,y(0)=2

(1 + x^{5}) y^{^{'}} + 5 x^{4} y = 13 x^{4}, y (0) = 2

y = \frac{13 x ^{5}}{5 ( 1 + x ^{5} )} + \frac{2}{1 + x ^{5}}

Solution steps

(1 + x^{5}) y^{'} (x) + 5 x^{4} y = 13 x^{4}

Solve linear ODE:

y = \frac{13 x ^{5}}{5 ( 1 + x ^{5} )} + \frac{2}{1 + x ^{5}}

y = \frac{13 x ^{5}}{5 ( 1 + x ^{5} )} + \frac{2}{1 + x ^{5}}

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e^{- 12 t} f + 12 e^{- 12 t} f^{^{'}} = - 4 e^{- 14 t}

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What is the solution for (1+x^5)y^'+5x^4y=13x^4,y(0)=2 ?
The solution for (1+x^5)y^'+5x^4y=13x^4,y(0)=2 is y=(13x^5)/(5(1+x^5))+2/(1+x^5)