What is the solution for (x+1)y^'=-2y+(x+1)^{5/2},y(0)= 11/9 ?

The solution for (x+1)y^'=-2y+(x+1)^{5/2},y(0)= 11/9 is y=(2(x+1)^{5/2})/9+1/(x^2+2x+1)

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(x+1)y^'=-2y+(x+1)^{5/2},y(0)= 11/9

(x + 1) y^{^{'}} = - 2 y + (x + 1)^{\frac{5}{2}}, y (0) = \frac{11}{9}

y = \frac{2 ( x + 1 ) ^{\frac{5}{2}}}{9} + \frac{1}{x ^{2} + 2 x + 1}

Solution steps

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

Solve linear ODE:

y = \frac{2 ( x + 1 ) ^{\frac{5}{2}}}{9} + \frac{1}{x ^{2} + 2 x + 1}

y = \frac{2 ( x + 1 ) ^{\frac{5}{2}}}{9} + \frac{1}{x ^{2} + 2 x + 1}

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What is the solution for (x+1)y^'=-2y+(x+1)^{5/2},y(0)= 11/9 ?
The solution for (x+1)y^'=-2y+(x+1)^{5/2},y(0)= 11/9 is y=(2(x+1)^{5/2})/9+1/(x^2+2x+1)