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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(z) + b = 0\; \text{ where } y(z) = {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(z) + b = 0\; \text{ where } y(z) = {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
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Powab{a}^{b} Power
Sinsin(z)\sin(z) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("f1691f"),
    Formula(Where(Equal(Add(Add(ComplexDerivative(y(z), For(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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2019-11-19 15:10:20.037976 UTC