Question

The differential equation of the family of curves $y=A{e}^{3x}+B{e}^{5x}$,where A and B are arbitrary constants, is

• A. $\frac{d^{2}y}{d{x}^2}+8\frac{dy}{dx}+15y=0$
  
• B. $\frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}+15y=0$
  
• C. $\frac{d^{2}y}{d{x}^2}-\frac{dy}{dx}+y=0$
• D. $Noneofthese$

Answer 1

The correct option is B $\frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}+15y=0$


$y=A{e}^{3x}+B{e}^{5x}\Rightarrow \frac{dy}{dx}=3A{e}^{3x}+5B{e}^{5x}\Rightarrow \frac{d^{2}y}{d{x}^2}=9A{e}^{3x}+25B{e}^{5x}$
$\Rightarrow \frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}+15y=0$ (By inspection)