Solving Initial Value Problems
Solve the initial value problems in Exercises 15–20.
dy/dt + 2y = 3, y(0) = 1

First-Order Linear Equations

Solve the differential equations in Exercises 1–14.

(t-1)³ ds/dt + 4(t-1)²s = t+1, t >1

Use Euler’s method with dx = 0.5 to estimate y(5) if y′ = y²/√x and y(1) = −1. What is the exact value of y(5)?

First-Order Linear Equations

Solve the differential equations in Exercises 1–14.

xdy/dx + y = e ͯ, x > 0

Solve the Bernoulli equations in Exercises 29–32.

y' - y = xy²

What integral equation is equivalent to the initial value problem y' = f(x), y(x₀) = y₀?

Using Euler’s Method

In Exercises 15–20, use Euler’s method to calculate the first three approximations to the given initial value problem for the specified increment size. Calculate the exact solution and investigate the accuracy of your approximations. Round your results to four decimal places.

y' = 2y/x, y(1) = -1, dx = 0.5