Differential Equations

Homogeneous ODE â€” v = y/x Substitution

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

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Inputs

ODE Preset (dy/dx =)

Initial Condition xâ‚€ (xâ‚€ > 0)

Initial Condition yâ‚€ = y(xâ‚€)

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

Select a preset above.

Particular Solution y(x) + Slope Field