Which of the following differential equation y=c_1e^x+c_2e^(−x) as a general solution? A. (d^2 y)/(dx^2)+y=0 B. (d^2 y)(dx^2)−y=0 C. (d^2 y)(dx^2)+1=0 D. (d^2y)(dx^2)−1=0

Anabella Gilbert

Anabella Gilbert

Answered question

2023-01-10

Which of the following differential equation y=c1ex+c2e-x as a general solution?
A. d2ydx2+y=0
B. d2ydx2-y=0
C. d2ydx2+1=0
D. d2ydx2-1=0

Answer & Explanation

kwabenzafvf

kwabenzafvf

Beginner2023-01-11Added 11 answers

Explanation for the correct option:
Option B.d2ydx2-y=0
Consider y=c1ex+c2e-x.
Differentiate the provided function in relation to both sides of x.
dydx=ddxc1ex+c2e-xdydx=ddxc1ex+ddxc2e-xdydx=c1ex-c2e-xddxc1ex=c2ddxex
Again differentiate both sides with respect to x to determine the second derivative:
d2ydx2=ddxc1ex-c2e-xd2ydx2=ddxc1ex-ddxc2e-xd2ydx2=c1ex+c2e-x[ddxe-x=-e-x]d2ydx2=yd2ydx2-y=0
Hence, option (B) is correct.
Explanation for incorrect option:
Since the required second derivative of the solution of the given function is not equivalent value mention Option (A), Option (C), and Option (D)
Hence Option (A), Option (C) and Option (D) are incorrect options
Hence Option(B) is the correct answer.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?