How would you use the Integration Factor method to solve an ordinary first-order linear differential equation?

The word "ordinary" means that there are only two variables, "first-order" means that the highest derivative is the first derivative and "linear" means that the highest power of the function variable is 1. Therefore, the Integration Factor method is applicable.First, you get values with the function variable (y for dy/dx) on the left and the parameter variable (x for dy/dx) on the right. You integrate the coefficient of y with respect to x to get the "Integration Factor (IF)". Then, multiply both sides of the differential equation by IF. Here, you get y multiplied by IF equal to the integral of the right hand side of the new differential equation. Solve the integral and divide by IF to get y(x).

KC
Answered by Kelvin C. Further Mathematics tutor

2541 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Prove by induction that, for all integers n >=1 , ∑(from r=1 to n) r(2r−1)(3r−1)=(n/6)(n+1)(9n^2 -n−2). Assume that 9(k+1)^2 -(k+1)-2=9k^2 +17k+6


Find the nth roots of unity.


What are imaginary numbers and why do we use them?


A spring with a spring constant k is connected to the ceiling. First a weight of mass m is connected to the spring. Deduce the new equilibrium position of the spring, find its equation of motion and hence deduce its frequency f.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning