1. Find the general solution of linear differential equation
dy/dx – y/(x+1) = x
2. Given that (x) dy/dx – 2y = x^3 ln x, find y in terms of x such that y=2 at x=1.
Please help me to solve these.
1. Multiplying by (x+1)^-1 gives:
(x+1)^-1 dy/dx - y (x+1)^-2 = x(x+1)^-1
y(x+1)^1 d/dx = ∫ x(x+1)^-1
How can I integrated this?
2. After Integrating:
yx^-2 = x(ln x - 1) + C
Since y=2 at x=1 this gives:
C=3
That is: yx^-2 = x(ln x - 1) + 3
So y =x^3 (ln x - 1) + 3 x^2
Is it right?