In Problems 1-8, find a general solution to the differential equation using the method of variation of parameters. 1. y′′+y=sect 2. y′′+4y=tan2t 3. y′′+2y′+y=e−t 4. y′′−2y′+y=t−1et 5. y′′+9y=sec2(3t) 6. y′′(θ)+16y(θ)=sec4θ 7. y′′+4y′+4y=e−2tlnt 8. y′′+4y=csc2(2t)

Question.4: The given differential equation: The associated auxiliary equation will be given by: For t...

Resuelto In Problems 1-8, find a general solution to the

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Pregunta: In Problems 1-8, find a general solution to the differential equation using the method of variation of parameters. 1. y′′+y=sect 2. y′′+4y=tan2t 3. y′′+2y′+y=e−t 4. y′′−2y′+y=t−1et 5. y′′+9y=sec2(3t) 6. y′′(θ)+16y(θ)=sec4θ 7. y′′+4y′+4y=e−2tlnt 8. y′′+4y=csc2(2t)
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Paso 1
Question.4: The given differential equation:
$\begin{aligned} y^{″} - 2 y + y & = t^{- 1} e^{t} \end{aligned}$
The associated auxiliary equation will be given by:
$\begin{matrix} \begin{aligned} λ^{2} - 2 λ + 1 & = 0 \\ λ_{1} = λ_{2} & = 1 \end{aligned} \end{matrix}$
For t...
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