gate 2016 engineering mathematics q30 of ce of paper 1 on differential equations

1. GATE-2016
MATHEMATICS
CE-PAPER I
DIFFERENTIAL EQUATIONS

4. We have from the differential
equation
D4 + 3D2 =0 where D=d/dx
THIS QUADRATIC EQUATION
YIELDS
THE ROOTS 0,0, AND TWO
IMAGINARY ROOTS

5. • THE ROOT 0 WITH A
MULTIPLICITY OF 2
DEMANDS THAT WE HAVE
IN THE SOLUTION—
• constant1 +Xconstant2+---

6. • THE ROOT 0 WITH A
MULTIPLICITY OF 2
DEMANDS THAT WE HAVE
IN THE SOLUTION—
• constant1 +Xconstant2+---
This rules out choices B and
C

7. • Now consider the particular
• integral part
• We have ---+3D2 y+----
• If we substitute 3x4 for y
• we will get the 108x2
• This is what we need
• We cannot susbstitute 5x4