Cauchy–Euler Equation Solver: Step-by-Step Solutions

Substitution x = eᵗ, indicial equation, and nonhomogeneous terms in powers of x and ln x. Every step of the solution is shown, as you would write it on paper, using exact fractions.

What it solves

Solve $a{x}^2{y}^{\prime \prime }+bx{y}^{\prime }+cy=F(x)$ (three coefficients) or $a{x}^3{y}^{\prime \prime \prime }+b{x}^2{y}^{\prime \prime }+cx{y}^{\prime }+dy=F(x)$ (four coefficients) for $x>0$. $F$ may contain terms like 5x^3 or 2x ln(x), or leave it empty.

How to use it

1. Enter your own numbers or functions in the boxes (an example is already filled in, or press Random example).
2. Check the equation preview, then press Solve step by step.
3. Reveal the solution one step at a time with Next step, or show everything at once.

Need the theory first? Read Section 4.5: The Cauchy–Euler Equation, which explains the method in small steps with worked examples and exercises, then come back and test yourself with the Chapter 4 quiz.

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