Differential equations For case 3 of solving second order differential equations with constant coefficients, when the roots of the associated characteristic equation are repeated real roots. The solution is given by: y1=e^rx and y2=u(x)e^rx. Prove that if y2 is a solution of the equation ay′′+by′+cy=0, then u(x)=x.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 15E: Find the general solution for each differential equation. Verify that each solution satisfies the...
Question
Differential equations For case 3 of solving second order differential equations with constant coefficients, when the roots of the associated characteristic equation are repeated real roots. The solution is given by: y1=e^rx and y2=u(x)e^rx. Prove that if y2 is a solution of the equation ay′′+by′+cy=0, then u(x)=x.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,