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Solve the initial value problem y" + 5y = 0?

User Simo Ahava
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Final answer:

To solve the initial value problem y'' + 5y = 0, we assume a solution of the form y = e^(rx) and find the roots of the characteristic equation. Since the roots are complex, the general solution is y = Ae^(√5x)i + Be^(-√5x)i.

Step-by-step explanation:

The given equation is a second-order linear homogeneous differential equation. To solve this equation, we assume a solution of the form y = e^(rx), where r is a constant. Substituting this into the equation, we get the characteristic equation r^2 + 5 = 0. Solving this equation gives us r = ±√(-5). Since the discriminant is negative, the roots are complex. Therefore, the general solution to the equation is y = Ae^(√5x)i + Be^(-√5x)i, where A and B are constants.

User Stephen Morrell
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