(x+1) dy/dx= x (y^2+1)

Question

Solve by variable separation method.

Answer 1

QUESTION: (x+1) dy/dx= x (y^2+1)

Solve by variable separation method.

put all the y's on the left anf all the x's on the right.

dy/(y^2+1) = x.dx/(x+1)

now integrate both sides.

Int 1/(y^2+1) dy = Int x/(x+1) dx

LHS

Int 1/(y^2+1) dy = atan(y)

RHS

Int x/(x+1) dx = Int 1 - 1/(x+1) dx = x - ln(x+1) - lnA   (lnA = const of integration)

Int x/(x+1) dx = x - ln(A(x+1))

Equating both sides,

atan(y) = x - ln(A(x+1))

y = tan{x - ln(A(x+1))}