Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If the solution of differential equation x 2 
+ 2x 
= 12y is y = Ax m + Bx –n then find the value of m + n, if m & n ∈ N.
Text Solution
Verified by ExpertsThe correct answer is:
7
Ans. 7
Sol. y = Ax m + Bx –n ⇒ 
= Amx
m–1 – nBx –n–1 ⇒ 
= Am (m –1) x
m–2 + n (n +1) Bx –n –2 Putting these values in x
2 
+ 2x 
= 12y
We have = m (m + 1) Ax m + n (n –1) Bx –n = 12 (Ax
m + Bx –n )
⇒ m (m +1) = 12 or n (n –1) = 12
⇒ m = 3, –4 or n = 4, –3
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