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vodomira [7]
4 years ago
15

Find a general solution of y" – 4y = 0.

Mathematics
1 answer:
soldier1979 [14.2K]4 years ago
6 0

Answer:

y = C_{1}e^{2x} + C_{2}e^{-2x}

Step-by-step explanation:

We are given the differential equation: y'' - 4y = 0

We have to find the general solution.

The auxiliary equation for the above differential equation can be written as:

m² - 4 = 0

We solve for m.

⇒m² = 4

⇒m = ±2

⇒m_{1} = +2 and m_{2} = -2

Thus, we have two distinct roots or we have two distinct values of m.

Thus, the general solution will be of the form:

y = C_{1}e^{m_{1}x} + C_{2}e^{m_{2}x}

y = C_{1}e^{2x} + C_{2}e^{-2x}

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