What is the solution for 2yy^'+2=y^2+2x,y(0)=9 ?

The solution for 2yy^'+2=y^2+2x,y(0)=9 is y=sqrt(-2x+81e^x)

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2yy^'+2=y^2+2x,y(0)=9

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 9

y = - 2 x + 81 e^{x}

Solution steps

2 y y^{'} (x) + 2 = y^{2} + 2 x

Solve Bernoulli ODE:

y = - 2 x + 81 e^{x}

y = - 2 x + 81 e^{x}

\int - 5 d x

\int_{5}^{8} (13 - 2 x) d x

\frac{d}{d x} (2 x^{2} + 3 x)

\int (\frac{5}{3})^{x} d x

What is the solution for 2yy^'+2=y^2+2x,y(0)=9 ?
The solution for 2yy^'+2=y^2+2x,y(0)=9 is y=sqrt(-2x+81e^x)