Ordinary Differential Equation

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Introduction to ODEs and their classifications.

Common Forms

First Order Linear

y' + P(x)y = Q(x)

Separable

dy/dx = g(x)h(y)

Bernoulli

y' + P(x)y = Q(x)yⁿ

Classification

OrderHighest Derivativee.g. y'' is 2nd order

LinearityLinear vs Non-linearNo y² or sin(y) terms

HomogeneityHomogeneousIf Q(x) = 0 in linear form

About this calculator

What is an ODE?

An Ordinary Differential Equation (ODE) is an equation containing a function of one independent variable and its derivatives. Solving an ODE typically involves finding the function y = f(x) that satisfies the equation.

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Pro Tips

Order: The highest derivative present.
Degree: The power of the highest derivative.
Linearity: Dependent variable y and its derivatives appear linearly.

Fun Facts

"ODEs model growth, decay, oscillations, and more."
"Newton's Second Law (F=ma) is a second-order ODE."

Formula: F(x, y, y', y'', ..., y⁽ⁿ⁾) = 0