Life is sad

Literally differentiate the solution they give you and plug it in, why do you think you actually have to solve that DE, am I being baited?

Integrate it you retard.

Its just an application of the fundamental theorem of calculus.

No shit sherlock the problem what the fuck do i do after that

I legitimately can't understand what difficulty you are having here. Why post this? What did he mean by this?

this

To solve a quadratic equation you use
en.wikipedia.org/wiki/Quadratic_formula

I did and that was why I called you a brainlet

oh shit im a brainlet

You didn't have to do any of this, it's a show that question, you can just plug in f(x), show it equals 0, and be done with it.

Technically, the way the question is worded, it could be interpreted as "show that f(x) must be such and such function in this initial value problem," rather than, "show that f(x) could be such and such function in this initial value problem." If the latter is the correct interpretation, then checking the two conditions is good enough. If the former is the correct interpretation, then, either you have to prove ln(x+sqrt(x^2 + 1)) is the only solution by integration and the quadratic formula, or use the uniqueness and existence theorems to show that a single solution of the initial value problem exists, and prove that the provided solution fits the bill.

this is the correct answer. the uniqueness and existence theorem for ODE really does save lives.

reported for being homework