What is the solution for (dy)/(dx)=((y+x))/((y-x)),y(0)=1 ?

The solution for (dy)/(dx)=((y+x))/((y-x)),y(0)=1 is y=x+sqrt(2x^2+1)

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(dy)/(dx)=((y+x))/((y-x)),y(0)=1

\frac{d y}{d x} = \frac{( y + x )}{( y - x )}, y (0) = 1

y = x + 2 x^{2} + 1

Solution steps

\frac{d y}{d x} = \frac{( y + x )}{( y - x )}

Solve exact ODE:

y = x + 2 x^{2} + 1

y = x + 2 x^{2} + 1

What is the solution for (dy)/(dx)=((y+x))/((y-x)),y(0)=1 ?
The solution for (dy)/(dx)=((y+x))/((y-x)),y(0)=1 is y=x+sqrt(2x^2+1)