Question

Which of the following differential equations has y= c1ex+c2e-x as the general solution?

• A. $\frac{d^2y}{dx^2}+y=0$
• B. $\frac{d^2y}{dx^2}-y=0$
• C. $\frac{d^2y}{dx^2}+1=0$
• D. $\frac{d^2}{dx^2}-1=0$

Answer 1

Answer: (B)

$\frac{d^2y}{dx^2}-y=0$

Answer 2

The given equations is:

y= c1ex+c2e-x ...(1)

Differentiating with respect to x, we get:

$\frac{dy}{dx}=c_1e^x-c_2e^{-x}$

Again, differentiating with respect to x, we get:

$\frac{d^2y}{dx^2}=c_1e^x-c_2e^{-x}$

$\Rightarrow \frac{d^2y}{dx^2}=y$

$\Rightarrow \frac{d^2y}{dx^2}-y=0$

This is the required differential equation of the given equation of curve.

Hence, the correct answer is B.