Constant-coefficient second-order linear ODEs

Trying an exponential yields the characteristic equation, then three root cases to handle: distinct real, repeated, and complex giving oscillatory solutions.

Notes on Diffy Qs: Differential Equations for Engineers, Constant-coefficient second-order linear ODEs

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7 exercises

Exercise 101

Find the general solution to $y''+4y'+2y=0$ .

2.5

Exercise 102

Find the general solution to $y''-6y'+9y=0$ .

2.5

Exercise 103

Find the solution to $2y''+y'+y=0$ , $y(0) = 1$ , $y'(0)=-2$ .

2.5

Exercise 104

Find the solution to $2y''+y'-3y=0$ , $y(0) = a$ , $y'(0)=b$ .

2.5

Exercise 105

Find the solution to $z''(t) = -2z'(t)-2z(t)$ , $z(0) = 2$ , $z'(0)= -2$ .

2.5

Exercise 106

Find the solution to $y''-(\alpha+\beta) y' + \alpha \beta y=0$ , $y(0) = a$ , $y'(0)=b$ , where $\alpha$ , $\beta$ , $a$ , and $b$ are real numbers, and $\alpha \neq \beta$ .

2.5

Exercise 107

Construct an equation such that $y = C_1 e^{3x} + C_2 e^{-2x}$ is the general solution.

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