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Hi

I have differential equation

[tex]y'' + p(x)\cdot x' + q(x)y = 0[/tex] which have two solutions [tex]y_1(x)[/tex] and [tex]y_2(x)[/tex] where [tex]y_1(x) \neq 0[/tex]

show that [tex]y_2(t) = y_1(t)\int_{t_0}^{t} \frac{1}{y_1(s)^2} e^{-\int_{t_0}^s p(r) dr} ds[/tex] is also a solution.

I know that wronskian for this is defined

[tex]w(y_1,y_2)(t) = c \cdot e^{-\int p(t) dt}[/tex] according to Abels identity theorem.

My question do I use this property of theorem and properties of the Wronskian to derive c?

## Homework Statement

I have differential equation

[tex]y'' + p(x)\cdot x' + q(x)y = 0[/tex] which have two solutions [tex]y_1(x)[/tex] and [tex]y_2(x)[/tex] where [tex]y_1(x) \neq 0[/tex]

show that [tex]y_2(t) = y_1(t)\int_{t_0}^{t} \frac{1}{y_1(s)^2} e^{-\int_{t_0}^s p(r) dr} ds[/tex] is also a solution.

## Homework Equations

I know that wronskian for this is defined

[tex]w(y_1,y_2)(t) = c \cdot e^{-\int p(t) dt}[/tex] according to Abels identity theorem.

## The Attempt at a Solution

My question do I use this property of theorem and properties of the Wronskian to derive c?

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