Question

Two differential equation of the family of curves $y=e^x(A\cos x+B\sin x)$, where $A,B$ are arbitrary constant, 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

The correct option is C $n=1,m=2$

$y=e^x(A\cos x+B\sin x)$
$\frac{dy}{dx}=e^x(-A\sin x+B\cos x)+e^x(A\cos x+B\sin x)$
$\frac{dy}{dx}=e^x(-A\sin x+B\cos x)+y$
$\frac{d^{2}y}{{dx}^2}=e^x(-A\cos x-B\sin x)+e^x(-A\sin x+B\cos x)+\frac{dy}{dx}$
$\frac{d^{2}y}{{dx}^2}=-y+\frac{dy}{dx}-y+\frac{dy}{dx}$
$\frac{d^{2}y}{{dx}^2}=-2y+2\frac{dy}{dx}$
Order m=2, degree n =1