What is the solution for (dy)/(dx)=((2x+1))/(2y) ?

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

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(dy)/(dx)=((2x+1))/(2y)

\frac{d y}{d x} = \frac{( 2 x + 1 )}{2 y}

y = x^{2} + x + c_{1}, y = - x^{2} + x + c_{1}

Solution steps

\frac{d y}{d x} = \frac{( 2 x + 1 )}{2 y}

Solve separable ODE:

y = x^{2} + x + c_{1}, y = - x^{2} + x + c_{1}

y = x^{2} + x + c_{1}, y = - x^{2} + x + c_{1}

9 x (2 x^{2} + 1)

\int (x ln (x))^{2} (\frac{1}{x ^{2}}) d x

2 x

\int 9 t^{2} + 4 d t

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

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