Question

Which of the following differential equations has y= c₁e^x+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

The Correct Option is B

The given equations is:

y= c₁e^x+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.