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

The solution for (dy)/(dx)x= 2/3 (y-1)^{3/2} is y=(36)/(4ln^2(x)+12c_{1)ln(x)+9c_{1}^2}+1

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(dy)/(dx)x= 2/3 (y-1)^{3/2}

\frac{d y}{d x} x = \frac{2}{3} (y - 1)^{\frac{3}{2}}

y = \frac{36}{4 ln ^{2} ( x ) + 12 c _{1} ln ( x ) + 9 c _{1}^{2}} + 1

Solution steps

\frac{d y}{d x} x = \frac{2}{3} (y - 1)^{\frac{3}{2}}

Solve separable ODE:

y = \frac{36}{4 ln ^{2} ( x ) + 12 c _{1} ln ( x ) + 9 c _{1}^{2}} + 1

y = \frac{36}{4 ln ^{2} ( x ) + 12 c _{1} ln ( x ) + 9 c _{1}^{2}} + 1

(x - 13) (x - 3) y^{^{'}} = y

\frac{d x}{d y} = 3 e^{2 x - 3 y}

x d y - (y + 4) d x = 0

\frac{d y}{d x} = 14 e^{5 x - y}, y (0) = 0

\frac{d y}{d t} = \frac{( 3 t ^{2} + 4 t + 2 )}{2 ( y - 1 )}

What is the solution for (dy)/(dx)x= 2/3 (y-1)^{3/2} ?
The solution for (dy)/(dx)x= 2/3 (y-1)^{3/2} is y=(36)/(4ln^2(x)+12c_{1)ln(x)+9c_{1}^2}+1