Class 12

Math

Calculus

Differential Equations

If y=e4x+2e−x satisfies the relation d3ydx3+Adydx+By=0, then values of A and B respectively are:

- -13, 14
- -13, -12
- -13, 12
- 12, -13

**Correct Answer: ** Option(b)

**Solution: **[b] Given y=e4x+2e−x Differentiating we get dydx=4e4x−2e−x⇒d2ydx2=16e14x+2e−x ⇒d3ydx3=64e4x−2e−x Putting these values in d3ydx3+Adydx+By=0 We have, (64+4A+B)e4x+(−2−2A+2B)e−x=0 ⇒64+4A+B=0,−2−2A+2B=0 Solving these eqs. we get A=−13,B=−12