Let f(x) be a positive function such that the area bounded by y=f(x), y=0 from x=0 to x=a>0 is e^(-a)+4 a²+a-1. Then the differential equation, whose general solution is y=c₁ f(x)+c₂, where c₁ and c₂ are arbitrary constants, is

(B) (8 eˣ+1) (d² y)/(d x²)+(d y)/(d x)=0

(A) (8 eˣ+1) (d² y)/(d x²)-(d y)/(d x)=0

(C) (8 eˣ-1) (d² y)/(d x²)-(d y)/(d x)=0

(D) (8 eˣ-1) (d² y)/(d x²)+(d y)/(d x)=0

Differential Equations: JEE Main 2024 Mathematics question

JEE Main 2024 · 8 Apr, Morning shift · Q3503

JEE Main 20248 Apr, Morning shiftMathematicsMediumDifferential Equations163× since 2002

Let

f(x)

be a positive function such that the area bounded by

y=f(x), y=0

from

x=0

x=a>0

e^{-a}+4 a^2+a-1

. Then the differential equation, whose general solution is

y=c_1 f(x)+c_2

, where

c_1

and

c_2

are arbitrary constants, is