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CGP EDU Academic Team
Published on: August 11, 2026
Solve the differential equation
y = (1 + p) x + ap 2 , where p = 
Text Solution
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Sol. The given differential equation is
y = (1 + p) x + ap 2 ... (i)
Differentiating both sides with respect to x, we get
= 1 + p + x 
+ 2ap 
⇒ p = 1 + p + x 
+ 2ap 
⇒ 0 = 1 + 
(x + 2ap)
⇒ 
+ x = –2ap ... (ii)
This is a linear differential equation having
I.F. = 
= e p Multiplying both sides of (ii) by e
p and integrating, we get
xe p = –2a 
⇒ xe p = –2a (p –1) e p + C ... (iii)
Eliminating p between (i) and (iii), we obtain the desired solution.
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