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Examples for

# Step-by-Step Differential Equations

Separable Equations#### See how to solve separable differential equations step by step:

First-Order Exact Equations#### Solve exact differential equations step by step:

#### Use an integrating factor to transform an equation into an exact equation:

Chini-Type Equations#### Solve a Riccati equation step by step:

#### Solve an Abel equation of the first kind with a constant invariant:

#### Solve a Chini equation with a constant invariant:

Reduction of Order#### Reduce to a first-order equation:

#### Derive the equation of a catenary curve step by step:

Higher-Order Equations#### See the steps for solving higher-order differential equations:

First-Order Linear Equations#### Solve first-order linear differential equations:

#### See the steps for using Laplace transforms to solve an ordinary differential equation (ODE):

Bernoulli Equations#### Explore the steps to solve Bernoulli equations:

General First-Order Equations#### See the steps for solving Clairaut's equation:

#### Solve d'Alembert's equation:

#### See how first-order ODEs are solved:

Euler–Cauchy Equations#### Solve Euler–Cauchy equations:

First-Order Substitutions#### Solve a first-order homogeneous equation through a substitution:

#### Learn the steps to make general substitutions:

Second-Order Constant-Coefficient Linear Equations#### Solve a constant-coefficient linear homogeneous equation:

#### Explore how to solve inhomogeneous constant-coefficient linear equations:

#### See the steps for using Laplace transforms to solve an ODE:

General Second-Order Equations#### Investigate the steps for solving second-order ODEs: