Question

The P.I. of $(3D^2+D-14)y=13e^{2x}$ is:

• A. $26x{e}^{2x}$
• B. $13x{e}^{2x}$
• C. $x{e}^{2x}$
• D. $\frac{x^2}{2}{e}^{2x}$

Answer 1

Answer: (C)

$x{e}^{2x}$

Let $f\left(D\right)=3D^2+D-14$ , which implies $f_{m=2}=12+2-14=0$ and $f_{m=2}^{\prime }=12+1=13$

We know that , for equation $(3D^2+D-14)y=13e^{mx}$ , if $f\left(m\right)=0$ and $f^1\left(m\right)\ne 0$ then the Principal solution is $13\frac{x{e}^{mx}}{f^{\prime }\left(m\right)}$

Here $m=2$ , so we get principal solution as $x{e}^{2x}$

Therefore the correct option is $C$