Solve a non-separable first-order differential equation by using a substitution to make it separable.

Vault Of Euclid

Solving a First-Order ODE with a Linear Substitution

Parametric equations and vector functions core

Solve \(y' = (x+y)^2\). (As usual, \(y' = \frac{dy}{dx}\).)

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

Basic differentiation
Separation of variables
Standard integration formulas, specifically for inverse trigonometric functions

What this problem tests

Tests the ability to recognize when a substitution can simplify a differential equation and the skill to carry out separation of variables and integration.

This problem is typical of an introductory differential equations course or a Calculus II course covering basic ODEs.

Solving a First-Order ODE with a Linear Substitution

What you need first

What this problem tests

More on Parametric equations and vector functions