# Fungrim entry: 984d9c

$y''(z) + y(z) = 0\; \text{ where } y(z) = {c}_{1} \sin(z) + {c}_{2} \cos(z)$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; {c}_{1} \in \mathbb{C} \;\mathbin{\operatorname{and}}\; {c}_{2} \in \mathbb{C}$
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
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
Sin$\sin(z)$ Sine
Cos$\cos(z)$ Cosine
CC$\mathbb{C}$ 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))))

## Topics using this entry

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

2021-03-15 19:12:00.328586 UTC