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' = 2xy + 2y, y(0) = 3, dx = 0.2

First-Order Linear Equations

Solve the differential equations in Exercises 1–14.

y' + (tanx)y = cos²x, -π/2 < x < π/2

First-Order Linear Equations

Solve the differential equations in Exercises 1–14.

(1+x)y' + y = √x

Integral Equations

In Exercises 7–12, write an equivalent first-order differential equation

and initial condition for y.

y = 1 + ∫₀ ͯ y(t) dt

Solving Initial Value Problems

Solve the initial value problems in Exercises 15–20.

(x+1) dy/dx - 2 (x² + x)y = exp(x²) / (x+1), x > -1, y(0) = 5

Solving Initial Value Problems

Solve the initial value problems in Exercises 15–20.

t dy/dt + 2y = t³, t > 0, y(2) = 1

Solve the Bernoulli equations in Exercises 29–32.

x²y' + 2xy = y³