First-Order Linear Equations
Solve the differential equations in Exercises 1–14.


(1+x)y' + y = √x

Show that (0, 0) and (c/d, a/b) are equilibrium points. Explain the meaning of each of these points.

Integral Equations

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

and initial condition for y.

y = ∫₁ ͯ 1/t dt

First-Order Linear Equations

Solve the differential equations in Exercises 1–14.

y' + (tanx)y = cos²x, -π/2 < x < π/2

Integral Equations

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

and initial condition for y.

y = 1 + ∫₀ ͯ y(t) dt

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

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