Question

Differential Equation.
Reduction of Order.

Answer 1

\[6y''+y'-y=0\]
When:
\[y_1=e^{\frac{ x }{ 3 }}\]

Answer 2

I've tried using the formula for reduction of orders.
\[y_2=y_1(x)=\int\limits_{}^{}\frac{ e^{-\int\limits_{}^{}P(x)dx} }{ y_1^2(x) }dx\]

Answer 3

Just came across another method apparently.
\[y = \ u(x)y_1\]

Answer 4

Just not familiar with it if it does hold for this equation.

Answer 5

yeah that's what i was reading, too http://tutorial.math.lamar.edu/Classes/DE/ReductionofOrder.aspx

Answer 6

I'm very out-of-practice with DE's, so I am reading it, myself

Answer 7

it holds for all such equations, it seems, so long as one solution is known