Question:
Forming a differential equation representing the curve y = a e3x + b e-2x by eliminating arbitrary constants a and b.
Forming a differential equation representing the curve y = a e3x + b e-2x by eliminating arbitrary constants a and b.
Options:
- y” + y’ – 6y = 0
- y” – y’ + 6y = 0
- y” + y’ + 6y = 0
- y” – y’ – 6y = 0
- y” + y’ – 6y = 0
- y” – y’ + 6y = 0
- y” + y’ + 6y = 0
- y” – y’ – 6y = 0
Correct Answer: d)
Explanation:
1
‘ ey = ae” + b di√iding by e™** ‘
‘ er —2e y= ae”.
1 Di√iding by e*
‘ el —2e%y=a ‘
spd
‘ ed (EL -2) =a
32 dy dy 3a (dy _
i ‘ CECI “(£—2y)=0
y ly _
‘ og —6y=0
1
‘ ey = ae” + b di√iding by e™** ‘
‘ er —2e y= ae”.
1 Di√iding by e*
‘ el —2e%y=a ‘
spd
‘ ed (EL -2) =a
32 dy dy 3a (dy _
i ‘ CECI “(£—2y)=0
y ly _
‘ og —6y=0