Solving Initial Value Problems
Solve the initial value problems in Exercises 15–20.


dy/dx + xy = x, y(0) = -6

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

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' = y²(1+2x), (y-1) = 1, dx = 0.5

First-Order Linear Equations

Solve the differential equations in Exercises 1–14.

e²ˣy' + 2e²ˣ y = 2x

Is either of the following equations correct? Give reasons for your answers.

a. (1/cosx) ∫ cos x dx = tan x + C

b. (1/cosx) ∫ cos x dx = tan x + C / cos x