Question

The differential equation of the family of curves $y=e^x(Acosx+Bsinx)$, where A, B are arbitrary constants, has the degree n and order m. Then

• A. $n=2,m=1$
• B. $n=2,m=2$
• C. $n=1,m=2$
• D. $n=1,m=1$

Answer 1

Answer: (C)

$n=1,m=2$

$y=e^x(Acosx+Bsinx)$
$\frac{dy}{dx}=e^x(-Asinx+Bcosx)+(Acosx+Bsinx)e^x$
$\frac{dy}{dx}=e^x(-Acos-Bsinx)+e^x(-Asinx+Bcosx)+\frac{dy}{dx}$
$\left(e^x\right(-Asinx+Bcosx)=\frac{dy}{dx}-y)$
$\therefore \frac{d^{2}y}{{dx}^2}=-y+\frac{dy}{dx}-y+\frac{dy}{dx}$
$\therefore (\frac{d^{2}y}{{dx}^2}-2\frac{dy}{dx}+2y=0)$
Differential equation
$\therefore$ Order = 2 = m
Degree = 1 = n