Question

The solution $\frac{dy}{dx}+y=e^x$ is

• A. $2y=e^{2x}+c$
• B. s $2y{e}^x=e^2+c$
• C. $2y{e}^x=e^{2x}+c$
• D. $2y{e}^{2x}=2e^x+c$

Answer 1

Answer: (C)

Given, differential equation is
$\frac{dy}{x}+y=e^x,$ which is of the form
$\frac{dy}{dx}+Py=Q$
Here, $P=1,Q=e^x$
$\therefore$ $IF=e^{\int Pdx}=e^{\int 1dx}=e^x$
Now, solution is $y.IF=\int Q.IFdx$
$\Rightarrow$ $y{e}^x=\int e^{2x}dx$
$\Rightarrow$ $y{e}^x=\frac{e^{2x}}{2}+c$
$\Rightarrow$ $2y{e}^x=e^{2x}+c$