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Examples for

Step-by-Step Differential Equations

Separable Equations

See how separable equations are solved:

First-Order Exact Equations

Solve 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:

RELATED EXAMPLES

  • Differential 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:

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