Question

If $y_1(x)$ and $y_2(x)$ are two solutions of $\frac{d y}{d x}+f(x) y=r(x)$ then $y_1(x)+y_2(x)$ is solution of:

• A. $\frac{d y}{d x}+f(x) y=0$
• B. $\frac{d y}{d x}+2 f(x) y=r(x)$
• C. $ \frac{d y}{d x}+f(x) y=2 r(x)$
• D. $\frac{d y}{d x}+2 f(x) y=2 r(x)$

Answer 1

Answer: (C)

$\frac{d y_1}{d x}+f y_1=r$
$\frac{d y_2}{d x}+f y_2=r$
Add $\frac{d}{d x}\left(y_1+y_2\right)+f\left(y_1+y_2\right)=2 r$
here $\frac{d y}{d x}+f(x) y=2 r$