What is the solution for (dy)/(dx)=(6y^3)/((3-2x)^2),y(0)=-1 ?

The solution for (dy)/(dx)=(6y^3)/((3-2x)^2),y(0)=-1 is y=-sqrt((2x)/(3(2x-1))-1/(2x-1))

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(dy)/(dx)=(6y^3)/((3-2x)^2),y(0)=-1

\frac{d y}{d x} = \frac{6 y ^{3}}{( 3 - 2 x ) ^{2}}, y (0) = - 1

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

Solution steps

\frac{d y}{d x} = \frac{6 y ^{3}}{( 3 - 2 x ) ^{2}}

Solve separable ODE:

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

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

\int \frac{t ^{2}}{2} d t

x \to 0 lim (\frac{ln ( x )}{x})

\int \frac{1}{( x ^{2} - 5 ) ^{\frac{3}{2}}} d x

tan (2) (x + 1)

\frac{d y}{d x} - 8 y = 5

What is the solution for (dy)/(dx)=(6y^3)/((3-2x)^2),y(0)=-1 ?
The solution for (dy)/(dx)=(6y^3)/((3-2x)^2),y(0)=-1 is y=-sqrt((2x)/(3(2x-1))-1/(2x-1))