Find the Wronskian of solutions y1 and y2 of the equation

[Fatima Hasan]

Homework Statement

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Homework Equations

$W(x) = C exp (∫ P(x) dx)$
$y''+P(x)y'+g(x)=0$

The Attempt at a Solution

Divide the origin equation by (x) to get the standard form of the homogeneous equation :
$y'' +\frac{3y'}{x} - \frac{3y}{x}$
$P(x) = \frac{3}{x}$
$exp (- ∫ \frac{3}{x}$
$= exp ( -3 ln (x))$
$= x^{-3}$
$W(x) = C x^{-3}$
Could someone check my answer please?

 

[Mark44]

Homework Statement

[/B]
View attachment 234516

Homework Equations

$W(x) = C exp (∫ P(x) dx)$
$y''+P(x)y'+g(x)=0$

The Attempt at a Solution

Divide the origin equation by (x)

No, you need to divide by $x^2$

to get the standard form of the homogeneous equation :
$y'' +\frac{3y'}{x} - \frac{3y}{x}$

The third term is incorrect. Also, you lost the = so you no longer have an equation.

$P(x) = \frac{3}{x}$
$exp (- ∫ \frac{3}{x}$
$= exp ( -3 ln (x))$
$= x^{-3}$
$W(x) = C x^{-3}$
Could someone check my answer please?

 

[Fatima Hasan]

No, you need to divide by $x^2$
The third term is incorrect. Also, you lost the = so you no longer have an equation.

I've solved it again , here's my work :

 

[Mark44]

Looks fine to me.