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Fungrim entry: 984d9c

y(z)+y(z)=0   where y(z)=c1sin(z)+c2cos(z)y''(z) + y(z) = 0\; \text{ where } y(z) = {c}_{1} \sin(z) + {c}_{2} \cos(z)
Assumptions:zCandc1Candc2Cz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, {c}_{1} \in \mathbb{C} \,\mathbin{\operatorname{and}}\, {c}_{2} \in \mathbb{C}
TeX:
y''(z) + y(z) = 0\; \text{ where } y(z) = {c}_{1} \sin(z) + {c}_{2} \cos(z)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, {c}_{1} \in \mathbb{C} \,\mathbin{\operatorname{and}}\, {c}_{2} \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Sinsin(z)\sin(z) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("984d9c"),
    Formula(Where(Equal(Add(ComplexDerivative(y(z), For(z, z, 2)), y(z)), 0), Equal(y(z), Add(Mul(Subscript(c, 1), Sin(z)), Mul(Subscript(c, 2), Cos(z)))))),
    Variables(z, Subscript(c, 1), Subscript(c, 2)),
    Assumptions(And(Element(z, CC), Element(Subscript(c, 1), CC), Element(Subscript(c, 2), CC))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC