What is the solution for (dy)/(dx)=18+30x+12y+20xy ?

The solution for (dy)/(dx)=18+30x+12y+20xy is y=(e^{10x^2+12x+c_{1}})/2-3/2

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(dy)/(dx)=18+30x+12y+20xy

\frac{d y}{d x} = 18 + 30 x + 12 y + 20 x y

y = \frac{e ^{10 x^{2} + 12 x + c_{1}}}{2} - \frac{3}{2}

Solution steps

\frac{d y}{d x} = 18 + 30 x + 12 y + 20 x y

Solve separable ODE:

y = \frac{e ^{10 x^{2} + 12 x + c_{1}}}{2} - \frac{3}{2}

y = \frac{e ^{10 x^{2} + 12 x + c_{1}}}{2} - \frac{3}{2}

y^{^{'}} + 32 \frac{y}{x} = 0

y^{^{'}} = \frac{x y sin ( x )}{y + 1}, y (0) = 1

x^{^{'}} = 1 - 3 x + x^{2}

u^{^{'}} = 3 e^{8 x - H (x)}

y^{^{'}} = \frac{( 3 x ^{2} + 4 x - 4 )}{2 y - 4}, y (1) = 3

What is the solution for (dy)/(dx)=18+30x+12y+20xy ?
The solution for (dy)/(dx)=18+30x+12y+20xy is y=(e^{10x^2+12x+c_{1}})/2-3/2