Question
Mathematics Question on Sets
The differential equation of the family of curves y=c1ex+c2e−x is:
A
(A) d2ydx2+y=0
B
(B) d2ydx2−y=0
C
(C) d3ydx3+y=0
D
(D) d4ydx4−1=0
Answer
(B) d2ydx2−y=0
Explanation
Solution
Explanation:
Given,y=c1ex+c2e−xDifferentiating w.r.t. xWe get,dydx=ddxc1ex+ddxc2e−x⇒dydx=c1ex−c2e−x⇒ddx(dydx)=ddx(c1ex−c2e−x)⇒d2ydx2=c1ex+c2e−x=y⇒d2ydx2−y=0Hence, the correct option is (B).