What is the solution for 7x^2y^'=y^'+9xe-y ?

The solution for 7x^2y^'=y^'+9xe-y is

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7x^2y^'=y^'+9xe-y

7 x^{2} y^{^{'}} = y^{^{'}} + 9 x e - y

y = e^{\frac{l n ( 7 x + 1 ) - l n ( 7 x - 1 )}{2 7}} \cdot \int \frac{9 e x ( ( 7 x - 1 ) ^{1 - 27} ) ^{\frac{1}{2 7}}}{( 7 x + 1 ) ^{\frac{1 + 2 7}{2 7}}} d x

Solution steps

7 x^{2} y^{'} (x) = y^{'} (x) + 9 x e - y

Solve linear ODE:

y = e^{\frac{l n ( 7 x + 1 ) - l n ( 7 x - 1 )}{2 7}} \cdot \int \frac{9 e x ( ( 7 x - 1 ) ^{1 - 27} ) ^{\frac{1}{2 7}}}{( 7 x + 1 ) ^{\frac{1 + 2 7}{2 7}}} d x

y = e^{\frac{l n ( 7 x + 1 ) - l n ( 7 x - 1 )}{2 7}} \cdot \int \frac{9 e x ( ( 7 x - 1 ) ^{1 - 27} ) ^{\frac{1}{2 7}}}{( 7 x + 1 ) ^{\frac{1 + 2 7}{2 7}}} d x

\int_{1}^{\infty} \frac{1}{x ^{2} + x} d x

\frac{d}{d x} (2^{x} ln^{2} (2))

9 x + 11, 7 x + 14, [23, 13]

\frac{\partial}{\partial y} (e^{y} sin (x))

What is the solution for 7x^2y^'=y^'+9xe-y ?
The solution for 7x^2y^'=y^'+9xe-y is