Solve the following initial value problem:
$\(\frac{dy}{dx}\)=2x-5$; $y\(\left\)(0\(\right\))=4$

Express the solutions of the initial value problems in Exercises 35 and 36 in terms of integrals.

dy/dx = sin x/x , y(5) = -3

In Exercises 5–8, show that each function is a solution of the given initial value problem.

7. Differential Equation: xy' + y = -sin(x), x>0

Initial condition: y(π/2) = 0

Solution candidate: y = cos(x)/x

Solve the initial value problems in Exercises 115–120.

115. dy/dx = 1/√(1 - x²), y(0) = 0

Solve the initial value problems in Exercises 115–120.

117. dy/dx = 1/(x√(x² - 1)), x > 1; y(2) = π

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 $y\left(t\right)$?

Solve the following initial-value problem using Laplace transforms: $y^{\text{'}\text{'}}+4y=0$, $y\left(0\right)=2$, $y^{\text{'}}\left(0\right)=0$. What is $y\left(t\right)$?