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

Sine