Question

If f(x) and g(x) are two solutions of the differential equation ay¢¢ + x² y¢ + y = e^x then f(x) – g (x) is solution of

• A. a² y¢¢ + y¢ + y = e^x
• B. ay¢¢ + y = e^x
• C. ay¢¢ + x² y¢ + y = 0
• D. y¢¢ + x² y¢ + y = 0

Answer 1

Answer: (C)

ay¢¢ + x² y¢ + y = 0

Answer 2

Since f(x) and g (x) are solution of given differential

equation

a f ¢¢ (x) + x² f ¢(x) + f(x) = e^x ….(i)

& ag¢¢ (x) + x² g¢ (x) + g(x) = e^x …….(ii)

(i) – (ii) given

a [f ¢¢ (x) – g¢¢ (x)] + x² [f ¢ (x) – g¢ (x)]

+ [f ¢ (x) – g¢ (x)] = 0