Question

Solve completely the differentiial equation d2y/dx2−a2y=0

Answer 1

Answer on Question #69642 – Math – Differential Equations

Question

Solve completely the differential equation $\frac{d^2y}{dx^2} - a^2y = 0$ .

Solution

We have that $y'' - a^2y = 0$ is a differential equation of the second order with constant coefficients. Then the characteristic equation has the form

$$k ^ {2} - a ^ {2} = 0.$$

Thus $k_{1} = a$ and $k_{2} = -a$ .

Hence the general solution of the equation is

$$y = C _ {1} e ^ {- a x} + C _ {2} e ^ {a x}.$$

Answer: $y = C_{1}e^{-ax} + C_{2}e^{ax}$ .

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