For homogeneous differential equations, equations {indicial equation} {characteristic equation, solution} can find solutions using base e raised to a power. r^n + a1 * r^(n - 1) + a2 * r^(n - 2) + ... + an = 0, where n is equation order, and r is general-solution highest power of e. Indicial equations remove highest-power term from differential equations, reducing equation degree.
Factors {integrating factor} can multiply an equation to make equation homogeneous.
To solve homogeneous differential equations, isolate variables {method of separation of variables} {separation of variables method}. Roots are e^(q*x) * (a + b*x + c * x^2 + ...), where q is coefficient, x is independent variable, and a b c are coefficients.
3-Calculus-Differential Equation-Methods
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Date Modified: 2022.0225