What is the solution for (dy)/(dx)=2y+x^2+9 ?

The solution for (dy)/(dx)=2y+x^2+9 is y=-(x^2)/2-x/2-19/4+c_{1}e^{2x}

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(dy)/(dx)=2y+x^2+9

\frac{d y}{d x} = 2 y + x^{2} + 9

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{19}{4} + c_{1} e^{2 x}

Solution steps

\frac{d y}{d x} = 2 y + x^{2} + 9

Solve linear ODE:

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{19}{4} + c_{1} e^{2 x}

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{19}{4} + c_{1} e^{2 x}

\frac{d y}{d t} (t) = \frac{y}{25 t ^{2} + 1}

\int (t^{2} - 2) d t

f (x) = \frac{x ^{2}}{x - 5}

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

\frac{d}{d x} (3 (8 x^{2} - 4 x)^{4})

What is the solution for (dy)/(dx)=2y+x^2+9 ?
The solution for (dy)/(dx)=2y+x^2+9 is y=-(x^2)/2-x/2-19/4+c_{1}e^{2x}