What is the solution for (dy)/(dx)=sqrt(2+3y) ?

The solution for (dy)/(dx)=sqrt(2+3y) is y=(3(x^2+c_{1}^2))/4+(3c_{1}x)/2-2/3

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(dy)/(dx)=sqrt(2+3y)

\frac{d y}{d x} = 2 + 3 y

y = \frac{3 ( x ^{2} + c _{1}^{2} )}{4} + \frac{3 c _{1} x}{2} - \frac{2}{3}

Solution steps

\frac{d y}{d x} = 2 + 3 y

Solve separable ODE:

y = \frac{3 ( x ^{2} + c _{1}^{2} )}{4} + \frac{3 c _{1} x}{2} - \frac{2}{3}

y = \frac{3 ( x ^{2} + c _{1}^{2} )}{4} + \frac{3 c _{1} x}{2} - \frac{2}{3}

What is the solution for (dy)/(dx)=sqrt(2+3y) ?
The solution for (dy)/(dx)=sqrt(2+3y) is y=(3(x^2+c_{1}^2))/4+(3c_{1}x)/2-2/3