Find the general solution of the differential equation.
-$\frac{d y}{d x}+2 x y=13 x$
A) $\frac{13}{2}+\mathrm{Me}^{-x^{2}}$
B) $\frac{13}{2}+2 x+M e^{-x^{2}}$
C) $\frac{13}{5}+\mathrm{Me}^{\mathrm{x}^{2}}$
D) $13+\mathrm{Me}^{\mathrm{x}^{2}}$

Question

Quizplus · Accepted Answer

The differential equation is a first-order linear differential equation. The integrating factor is $e^{\int 2x \, dx} = e^{x^2}$. Multiplying through by the integrating factor and solving gives the general solution $y = \frac{13}{2} + Me^{-x^2}$.

Find the General Solution of the Differential Equation dydx+2xy=13x\frac{d y}{d x}+2 x y=13 xdxdy​+2xy=13x

Find the General Solution of the Differential Equation $\frac{d y}{d x}+2 x y=13 x$