Find the general solution of the following differential equation.y″−6y′+13y=0

Brock Brown

Brock Brown

Answered

2021-12-31

Find the general solution of the following differential equation.
y6y+13y=0

Answer & Explanation

raefx88y

raefx88y

Expert

2022-01-01Added 26 answers

We have to find the general solution of the following differential equation.
y6y+13y=0
Let, y=Aemx be the trial solution of (1)
Then y=mAemx,ym2Aemx
The auxiliary equation becomes.
m26m+13=0
Using quadratic formula,
m=(6)±(6)241132(1)
m=6±36522
m=6±162
m=6±4i2
m=3±2i
So, the general solution is
y=e3xC4cos2x+c2sin2x,4,2 are arbitrary constants.
Bubich13

Bubich13

Expert

2022-01-02Added 36 answers

Get the equation in the form C1yn+C2yn1++Cn+1y=0
y6y+13y=0
Find the roots of the equation C1rn+C2rn1++Cn+1
r2+6r+13=0
r=3±2i
Your result is y=c1er1x+c2er2x++cnernx
y=e3x(c1cos(2x)+c2sin(2x))
karton

karton

Expert

2022-01-09Added 439 answers

y-6y+13y=0 We add all the numbers together, and all the variables 8y=0 y=0/8 y=0

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