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)".