Example Solutions for

Step-by-Step Differential Equations


Separable Equations

See how separable equations are solved:

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First-Order Linear Equations

Solve first-order linear equations:

See steps that use Laplace transforms to solve an ODE:

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First-Order Exact Equations

Solve exact equations:

Transform into an exact equation:

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Bernoulli Equations

Learn to solve Bernoulli equations:

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First-Order Substitutions

Apply a linear substitution:

Solve a first-order homogeneous equation through a substitution:

Make general substitutions:

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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:

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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:

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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:

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Reduction of Order

Reduce to a first-order equation:

Derive the equation of a catenary curve:

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Euler–Cauchy Equations

Solve Euler–Cauchy equations:

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General Second-Order Equations

See how second-order ordinary differential equations are solved:

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Higher-Order Equations

See the steps for higher-order equations:

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