Question
The solution of the differential equation (x+1) d y d x -y=e^ 3 x (x+1)^ 2 is
BITSAT
Mathematics
Differential Equations
2020
BITSAT 2020
BITSAT Mathematics Question (2020) — Solution
Options
- A. y=(x+1) e^ 3 x +c
- B. 3 y=(x+1)+e^ 3 x +c
- C. 3 y x+1 =e^ 3 x +c
- D. y e^ -3 x =3(x+1)+c
Answer
C. 3 y x+1 =e^ 3 x +c
Step-by-step solution
The given equation is d y d x - y x+1 =e^ 3 x (x+1) I.F. =e^ - 1 x+1 d x =e^ - (x+1) = 1 x+1 The solution is y ( 1 x+1 )= e^ 3 x (x+1) 1 x+1 d x+a y x+1 = e^ 3 x d x+a= e^ 3 x 3 +a 3 y x+1 =e^ 3 x +c, c=3 a
Related: Mathematics — Differential Equations · All PYQ Banks