Fungrim entry: 984d9c

y''(z) + y\!\left(z\right) = 0\; \text{ where } y\!\left(z\right) = {c}_{1} \sin\!\left(z\right) + {c}_{2} \cos\!\left(z\right)

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\!\left(z\right) = 0\; \text{ where } y\!\left(z\right) = {c}_{1} \sin\!\left(z\right) + {c}_{2} \cos\!\left(z\right)

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
`Derivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Derivative
`Sin`	$\sin\!\left(z\right)$	Sine
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("984d9c"),
    Formula(Where(Equal(Add(Derivative(y(z), Tuple(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