Solve the second-order differential equation

[Fatima Hasan]

Homework Statement

Homework Equations

The Attempt at a Solution

Can someone check my answer please ?

 

[Buzz Bloom]

Hi Fatima:

I suggest you take your solution

y(x) = x² - (1/3)x^-1​

and calculate y'(x) and y"(x).
Then substitute these three functions of x into corresponding terms of the original equation. After the substitution, the resulting equation should be reducible to

0 = 0​

if your and answer is correct.

Regards,
Buzz

 

[Fatima Hasan]

the resulting equation should be reducible to
0 = 0

I didn't get this equation , can you tell me where is my mistake please ?

 

[Mark44]

Thread moved.

 

[Mark44]

I didn't get this equation , can you tell me where is my mistake please ?

Your answer for $y_2(x)$ in the next-to-last line in post #1 is incorrect. Check the integration that you did.

 

[Fatima Hasan]

Your answer for $y_2(x)$ in the next-to-last line in post #1 is incorrect. Check the integration that you did.

$y_2(x) = x(x-\frac{1}{x})$
$y_2(x) = x^2-1$
$y(x) = C_1 y_1(x) + C_2y_2(x)$
$y(x) = C1 x + C_2 (x^2-1)$

 

[Mark44]

$y_2(x) = x(x-\frac{1}{x})$
$y_2(x) = x^2-1$
$y(x) = C_1 y_1(x) + C_2y_2(x)$
$y(x) = C1 x + C_2 (x^2-1)$

OK, now can you check that your solution is correct?

 

[Fatima Hasan]

OK, now can you check that your solution is correct?

Got it , thank you.