Solve: y'' - y' - 6y = 0. | Basic Mathematics 2081.2

Basic Mathematics2081.25 marksNumerical: second order differential equationSecond order linear differential equations

Solve: $y'' - y' - 6y = 0$ . [5]

Solve: $y'' - y' - 6y = 0$. [5]

Given data: - Differential equation: $y'' - y' - 6y = 0$ - Constant coefficients: $1, -1, -6$ - Homogeneous, second-order, linear ODE. All data present. Characteristic equation: Assume $y = e^{rx}$ , so $y' = re^{rx}$ , $y'' = r^2 e^{rx}$ . Substituting: $r^2 e^{rx} - r e^{rx} - 6 e^{rx} = 0$ Sinc...

Given data: - Differential equation: $y'' - y' - 6y = 0$ - Constant coefficients: $1, -1, -6$ - Homogeneous, second-order, linear ODE. All data present. Characteristic equation: Assume $y = e^{rx}$, so $y' = re^{rx}$, $y'' = r^2 e^{rx}$. Substituting: $$r^2 e^{rx} - r e^{rx} - 6 e^{rx} = 0$$ Sinc...

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