"Solve the higher order derivatives: y+4y+3y=0" solved and explained

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Answered question

2021-06-08

Solve the higher order derivatives:
y+4y+3y=0

insonsipthinye

Skilled2021-06-09Added 83 answers

Step 1
Consider the given equation.
y''+4y+3y=0
Make characteristic equation.

r^{2} + 3 r + r + 3 = 0

r(r+3)+1(r+3)=0
(r+3)(r+1)=0
r=-1, -3
Step 2
Make the solution.

y (x) = c_{1} e^{- x} + c_{2} e^{- 3 x}

Put the initial value.

2 = c_{1} e^{0} + c_{2} e^{0}

2 = c_{1} + c_{2} \dots (1)

And,

y^{'} (x) = - c_{1} e^{- x} - 3 c_{2} e^{- 3 x}

0 = - c_{1} - 3 c_{2}

c_{1} = - 3 c_{2}

Step 3
Put in the first equation.

- 3 c_{2} + c_{2} = 2

- 2 c_{2} = 2

c_{2} = 1

And,

c_{1} = 3

Put all the values in the equation.

y (x) = 3 e^{- x} - e^{- 3 x}

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