Question

Solve the diferential equation 2d2y/dx2+5dy7dx−12y=0

Answer 1

Answer on Question #69648 – Math – Differential Equations

Question

1. Solve the differential equation

$$2 \frac {d ^ {2} y}{d x ^ {2}} + 5 \frac {d y}{d x} - 1 2 y = 0$$

Solution

$$2 y ^ {\prime \prime} + 5 y ^ {\prime} - 1 2 y = 0$$

1. Construct a characteristic equation:

$$2 k ^ {2} + 5 k - 1 2 = 0;$$ $$k _ {1} = - 4; k _ {2} = \frac {3}{2};$$

2. The general solution of the differential equation:

$$y = C _ {1} e ^ {- 4 x} + C _ {2} e ^ {\frac {3}{2} x},$$

where $C_1$ and $C_2$ are arbitrary real constants.

Answer: $y = C_1 e^{-4x} + C_2 e^{\frac{3}{2}x}$.

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