What is the solution for (dy)/(dx)=sqrt(9/2 y) ?

The solution for (dy)/(dx)=sqrt(9/2 y) is y=(9x^2)/8+(3c_{1}x}{2sqrt(2)}+\frac{c_{1}^2)/4

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(dy)/(dx)=sqrt(9/2 y)

\frac{d y}{d x} = \frac{9}{2} y

y = \frac{9 x ^{2}}{8} + \frac{3 c _{1} x}{2 2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = \frac{9}{2} y

Solve separable ODE:

y = \frac{9 x ^{2}}{8} + \frac{3 c _{1} x}{2 2} + \frac{c _{1}^{2}}{4}

y = \frac{9 x ^{2}}{8} + \frac{3 c _{1} x}{2 2} + \frac{c _{1}^{2}}{4}

y y^{^{'}} = x e^{y^{2}}

y^{^{'}} - x y = 0

\frac{d y}{d x} = \frac{2 y}{( x + 1 ) + ( x + 1 ) ^{\frac{5}{2}}}

y^{^{'}} + 4 y = 0, y (0) = cos (2 t), y (0) = sin (2 t)

\frac{d y}{d x} = \frac{cos ( x )}{2 y}

What is the solution for (dy)/(dx)=sqrt(9/2 y) ?
The solution for (dy)/(dx)=sqrt(9/2 y) is y=(9x^2)/8+(3c_{1}x}{2sqrt(2)}+\frac{c_{1}^2)/4