Homework SourseFind values of m so that the function y xm is a solution of
Find values of m so that the function y = xm is a solution of the given differential equation.
x2y xy 3y = 0
Solution
y = x^m
=>
y\' = mx^(m-1), y\" = m(m-1)x^m-2)
=>
x^2 * m(m-1)x^(m-2) -x * mx^(m-1) -3x^m = 0
=>
m(m-1) -m -3 = 0
=>
m^2 -2m-3 = 0
=>
m = -1,3
![Find values of m so that the function y = xm is a solution of the given differential equation. x2y xy 3y = 0Solutiony = x^m => y\' = mx^(m-1), y\](/WebImages/28/find-values-of-m-so-that-the-function-y-xm-is-a-solution-of-1077122-1761565109-0.webp "Find values of m so that the function y = xm is a solution of the given differential equation. x2y xy 3y = 0Solutiony = x^m => y\' = mx^(m-1), y\")
