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Fungrim entry: f1691f

y(z)+a2y ⁣(z)+b=0   where y ⁣(z)=c1sin ⁣(az)+c2cos ⁣(az)ba2y''(z) + {a}^{2} y\!\left(z\right) + b = 0\; \text{ where } y\!\left(z\right) = {c}_{1} \sin\!\left(a z\right) + {c}_{2} \cos\!\left(a z\right) - \frac{b}{{a}^{2}}
Assumptions:zCandaC{0}andbCandc1Candc2Cz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, a \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, {c}_{1} \in \mathbb{C} \,\mathbin{\operatorname{and}}\, {c}_{2} \in \mathbb{C}
TeX:
y''(z) + {a}^{2} y\!\left(z\right) + b = 0\; \text{ where } y\!\left(z\right) = {c}_{1} \sin\!\left(a z\right) + {c}_{2} \cos\!\left(a z\right) - \frac{b}{{a}^{2}}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, a \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \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
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
Powab{a}^{b} Power
Sinsin ⁣(z)\sin\!\left(z\right) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("f1691f"),
    Formula(Where(Equal(Add(Add(Derivative(y(z), Tuple(z, z, 2)), Mul(Pow(a, 2), y(z))), b), 0), Equal(y(z), Sub(Add(Mul(Subscript(c, 1), Sin(Mul(a, z))), Mul(Subscript(c, 2), Cos(Mul(a, z)))), Div(b, Pow(a, 2)))))),
    Variables(z, a, b, Subscript(c, 1), Subscript(c, 2)),
    Assumptions(And(Element(z, CC), Element(a, SetMinus(CC, Set(0))), Element(b, 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.

2019-08-25 15:30:03.056001 UTC