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

3024 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

How do I sketch the locus of |z - 5-3i | = 3 on an Argand Diagram?


Show that the sum from 1 to n of 1/(2n+1)(2n-1) is equal to n/(2n+1) by Induction


A curve has equation y=(2-x)(1+x)+3, A line passes through the point (2,3) and the curve at a point with x coordinate 2+h. Find the gradient of the line. Then use that answer to find the gradient of the curve at (2,3), stating the value of the gradient


Using de Moivre's theorem demonstrate that "sin6x+sin2x(16(sinx)^4-16(sinx)^2+3)"


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:

© 2026 by IXL Learning