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Examples for

# Step-by-Step Differential Equations

### Separable Equations

#### See how separable equations are solved:

### First-Order Exact Equations

#### Transform into an exact equation:

### Chini-Type Equations

#### Solve a Riccati equation:

#### 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:

### Higher-Order Equations

#### See the steps for higher-order equations:

### First-Order Linear Equations

#### Solve first-order linear equations:

#### See steps that use Laplace transforms to solve an ODE:

### Bernoulli Equations

#### Learn 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 ordinary differential equations are solved:

### Euler–Cauchy Equations

#### Solve Euler–Cauchy equations:

### First-Order Substitutions

#### Apply a linear substitution:

#### Solve a first-order homogeneous equation through a substitution:

#### Make general substitutions:

### Second-Order Constant-Coefficient Linear Equations

#### Solve a constant-coefficient linear homogeneous equation:

#### Solve a constant-coefficient linear equation with multiple methods:

#### See steps that use Laplace transforms to solve an ODE:

### General Second-Order Equations

#### See how second-order ordinary differential equations are solved: