Topic: Engineering Mathematics
The differential equation satisfying $y=Ae^{3x}+Be^{2x}$ is
- A. $\frac{d^{2}y}{dx^{2}}+5\frac{dy}{dx}-6y=0$
- B. $\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}+6y=0$
- C. $\frac{d^{2}y}{dx^{2}}+5\frac{dy}{dx}+6y=0$
- D. $\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}-6y=0$
Answer: B. $\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}+6y=0$
Explanation: $D^{2}-5D+6=0$\n$D^{2}-3D-2D+6=0$\n$D(D-3)-2(D-3)=0$\n$D=2,3$\nThe general solution is:\n$y=Ae^{3x}+Be^{2x}$