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

The solution for (dy)/(dx)=(3x-2)^3e^{2y} is y=-(ln(-1/6 (3x-2)^4-c_{1}))/2

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

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

y = - \frac{ln ( - \frac{1}{6} ( 3 x - 2 ) ^{4} - c _{1} )}{2}

Solution steps

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

Solve separable ODE:

y = - \frac{ln ( - \frac{1}{6} ( 3 x - 2 ) ^{4} - c _{1} )}{2}

y = - \frac{ln ( - \frac{1}{6} ( 3 x - 2 ) ^{4} - c _{1} )}{2}

2 x d x + sin (y) d y = 0, y (1) = 0

q^{^{'}} (p) = \frac{5400 p ^{2} q ( p )}{( p ^{3} + 2 ) ^{2}}

\frac{d y}{d x} = 4 x^{3} + x^{3} y^{2}

\frac{d x}{d t} = - x^{2}

\frac{d y}{d t} = - y - y^{2}

What is the solution for (dy)/(dx)=(3x-2)^3e^{2y} ?
The solution for (dy)/(dx)=(3x-2)^3e^{2y} is y=-(ln(-1/6 (3x-2)^4-c_{1}))/2