# Does multiplying with integrating factor in ODE add extraneous solution?

For example, can we show that for first order linear differential equations, the equations before and after multiplying with integrating factor are equivalent? How? That is, the solution of one is the solution of other and vice versa.

• Are you using any textbook on ODE? Any textbook should have the proof that multiplying the ODE with integrating factor does not change the solutions of ODE. – Little Rookie Mar 12 '17 at 15:08