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

The solution for (dy)/(dx)=(3x-2)^3e^{2y},y=0,x=1 is y=-(ln(-((3x-2)^4)/6+7/6))/(2)

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(dy)/(dx)=(3x-2)^3e^{2y},y=0,x=1

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

y = - \frac{ln ( - \frac{( 3 x - 2 ) ^{4}}{6} + \frac{7}{6} )}{2}

Solution steps

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

Solve separable ODE:

y = - \frac{ln ( - \frac{( 3 x - 2 ) ^{4}}{6} + \frac{7}{6} )}{2}

y = - \frac{ln ( - \frac{( 3 x - 2 ) ^{4}}{6} + \frac{7}{6} )}{2}

\frac{d y}{d t} y = \frac{1}{2 81} \cdot 9

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

y^{^{'}} + \frac{y}{4} = 3, y (- 3) = 0

\frac{d P}{d t} = 7 Pt, P (1) = 6

3 y d x + x d y = 0

What is the solution for (dy)/(dx)=(3x-2)^3e^{2y},y=0,x=1 ?
The solution for (dy)/(dx)=(3x-2)^3e^{2y},y=0,x=1 is y=-(ln(-((3x-2)^4)/6+7/6))/(2)