initial valued problem

[Kenzo Nanak]

For the following initial valued problem (IVP), find the solution for ? > 0,
Comment on your results.
? ′′′ = 1 + 3 ? ? − 4 ? ? + 9√?.
?(1) = 8
?′(1) = 9
?′′(1) = 10

 

[Deleted member 4993]

For the following initial valued problem (IVP), find the solution for ? > 0,
Comment on your results.
? ′′′ = 1 + 3 ? ? − 4 ? ? + 9√?.
?(1) = 8
?′(1) = 9
?′′(1) = 10

Your problem is not displaying well.

May be you can post an image of your assignment - along with your work/thoughts.

 

[Kenzo Nanak]

Aright , I am going to post an image

 

[Kenzo Nanak]

 

[Deleted member 4993]

View attachment 25947

Hint:

y" = \(\displaystyle \int \left(1 + \frac{3}{x^2} - \frac{4}{x^3} + 9*\sqrt{x}\right ) dx \) ........... continue

 

[HallsofIvy]

I would write the equation as \(\displaystyle y'''= 1+ 3x^{-2}- 4x^{-3}+ 9x^{1/2}\).

Now , integrate to get y'' and use y''(1)= 10 to determine the "constant of integration".
Then integrate again to get y' and use y'(1)= 9 to determine the "constant of integration".
Finally integrate a third time to get y and use y(1)= 8 to determine the "constant of integration".