What is the solution for (dy)/(dx)=2y+x^2+7 ?

The solution for (dy)/(dx)=2y+x^2+7 is y=-(x^2)/2-x/2-15/4+c_{1}e^{2x}

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(dy)/(dx)=2y+x^2+7

\frac{d y}{d x} = 2 y + x^{2} + 7

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{15}{4} + c_{1} e^{2 x}

Solution steps

\frac{d y}{d x} = 2 y + x^{2} + 7

Solve linear ODE:

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{15}{4} + c_{1} e^{2 x}

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{15}{4} + c_{1} e^{2 x}

\int 16 x^{3} ln (x) d x

\int_{0}^{\frac{π}{4}} sin^{2} (x) d x

f (t) = \frac{1}{t}

\int (csc^{2} (x)) d x

f (x) = 4 x - x^{2}

What is the solution for (dy)/(dx)=2y+x^2+7 ?
The solution for (dy)/(dx)=2y+x^2+7 is y=-(x^2)/2-x/2-15/4+c_{1}e^{2x}