Question
The solution of the differential equation (x+1) d y d x -y=e^ 3 x (x+1)^2 is
The solution of the differential equation (x+1) d y d x -y=e^ 3 x (x+1)^2 is
C. 3 y x+1 =e^ 3 x +C
Given, d y d x - y x+1 =e^ 3 x (x+1) Above is linear differential equation of form aligned & d y d x +P x=Q \\ & IF =e^ P d x =e^ - 1 x+1 d x =e^ - (1+x) = 1 1+x aligned Solution will be aligned y IF & = Q IF d x \\ y 1 1+x & = e^ 3 x (x+1) 1 (1+x) d x \\ y 1+x & = e^ 3 x 3 +C^ \\ 3 y 1+x & =e^ 3 x +C^ [ C=3 C^ ] aligned
Related: Mathematics — Differential Equations · All PYQ Banks