7. Antiderivatives & Indefinite Integrals

Solve the following initial value problem:

$\(\frac{dy}{dx}\)=2x-5$; $y\(\left\)(0\(\right\))=4$

Using the acceleration function below, find the velocity function, if the velocity is v = 5 at time t = 2.

$a\(\left\)(t\(\right\))=-20$

Find the function $f\(\left\)(x\(\right\))$ that satisfies the following differential equation.

$f^{\(\prime\]\prime\)}\(\left\)(x\(\right\))=3x^2$; $f^{\(\prime\)}\(\left\)(0\(\right\))=1$; $f\(\left\)(1\(\right\))=3$

Consider the initial value problem: $y^{\mathrm{\text{'}\text{'}}}+16y=\cos \left(4t\right)$, with $y\left(0\right)=0$ and $y^{\mathrm{\text{'}}}\left(0\right)=0$. What is the particular solution $y\left(t\right)$?