Is This the Correct Method for Solving Differential Equations on Midterms?

[lyj0211]

Hi, this question came up in my midterm and I was hoping to know if this is the correct method or answer.

 

[SteamKing]

What do your trusty differentiation skills tell you? Where did f(x) come from?

 

[lyj0211]

What do your trusty differentiation skills tell you? Where did f(x) come from?

this is my answer, I am just not sure if it is correct.

 

[JJacquelin]

It's correct, I think.

 

[PeroK]

this is my answer, I am just not sure if it is correct.

Does that mean that you don't know how to differentiate the function you've found and check whether it satisfies the original equation?

 

[pasmith]

Hi, this question came up in my midterm and I was hoping to know if this is the correct method or answer.

You know you're immediately going to integrate with respect to $x$, so you can conserve symbols by writing "$u_x = \dfrac{(\frac 23 t^3 + t)}{1 + x} + f'(x)$ for an arbitrary differentiable $f(x)$".