SME
Differential Equations · Problem type
Separable, linear, both or neither
Use this for “Is y′ = y cos x separable, linear, or both? Which method solves it?”
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Can y′ be split as g(x)h(y)? Can it be written y′ + p(x)y = q(x)?
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Assumptions
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Separable: y′ = g(x)h(y), a function of x times a function of y, so dy ÷ h(y) = g(x) dx can be integrated on each side.
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Linear: y′ + p(x)y = q(x), with y and y′ only to the first power and never multiplied together or inside another function.
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An equation can be both (y′ = ky); solve it either way. Neither needs another method or a numerical one.
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