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

The solution for (dy)/(dx)=((3x+2y+1/3)^2)/(3x+2y+1/3) is y=-3/2 x-11/12+c_{1}e^{2x}

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(dy)/(dx)=((3x+2y+1/3)^2)/(3x+2y+1/3)

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

y = - \frac{3}{2} x - \frac{11}{12} + c_{1} e^{2 x}

Solution steps

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

Solve using substitution:

y = - \frac{3}{2} x - \frac{11}{12} + c_{1} e^{2 x}

y = - \frac{3}{2} x - \frac{11}{12} + c_{1} e^{2 x}

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What is the solution for (dy)/(dx)=((3x+2y+1/3)^2)/(3x+2y+1/3) ?
The solution for (dy)/(dx)=((3x+2y+1/3)^2)/(3x+2y+1/3) is y=-3/2 x-11/12+c_{1}e^{2x}