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

slaggingV

slaggingV

Answered question

2021-06-08

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

Answer & Explanation

insonsipthinye

insonsipthinye

Skilled2021-06-09Added 83 answers

Step 1
Consider the given equation.
y''+4y+3y=0
Make characteristic equation.
r2+3r+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)=c1ex+c2e3x
Put the initial value.
2=c1e0+c2e0
2=c1+c2(1)
And,
y(x)=c1ex3c2e3x
0=c13c2
c1=3c2
Step 3
Put in the first equation.
3c2+c2=2
2c2=2
c2=1
And,
c1=3
Put all the values in the equation.
y(x)=3exe3x

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