Differential Equations

Homogeneous ODE — v = y/x Substitution

Solve dy/dx = F(y/x) by substituting v = y/x (so y = vx, dy/dx = v + x·dv/dx), separating variables in v and x, integrating, then back-substituting.

Live Calculator · Step-by-Step · Differential Equations

Inputs

ODE Preset (dy/dx =)

Initial Condition x₀ (x₀ > 0)

Initial Condition y₀ = y(x₀)

Result

F(v) Form

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Separated Form in v, x

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General Solution

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Particular Solution

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Step-by-Step Work

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Particular Solution y(x) + Slope Field

Put It Into Practice

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