ORDINARY DIFFERENTIAL EQUATIONS 2y+12y+18y=0

Mary Hammonds

Mary Hammonds

Answered

2021-12-30

ORDINARY DIFFERENTIAL EQUATIONS
2y+12y+18y=0

Answer & Explanation

yotaniwc

yotaniwc

Expert

2021-12-31Added 34 answers

Step 1
Consider the details provided
2y12y+18y=0
Further, simplify.
y6y+9y=0
Immediately, enter the characteristic equation
r2+6r+9=0
Step 2
Now, find the factor of the equation.
r2+3r+3r+9=0
r(r+3)+3(r+3)=0
(r+3)2=0
r=3
Now, write the solution of the equation, as both the root are same.
y(x)=c1e3x+c2xe3x

alkaholikd9

alkaholikd9

Expert

2022-01-01Added 37 answers

The differential equation is given as
2y12y+18y=0
Corresponding auxiliary equation is given as
2m2+12m+18=0
2m2+6m+6m+18=0
2m(m+3)+6(m+3)=0
(2m+6)(m+3)=0
2(m+3)(m+3)=0
Roots of auxiliary equations are
m=3,3
Thus the general solution of the ordinary differential equation is
y=(C1+C2x)e3x
Vasquez

Vasquez

Expert

2022-01-09Added 457 answers

Given: 2y+12y+18y=0
Explanation:
2y+12y+18y=0
The equation can be written as
[2D2+12D+18]y=0 where D=ddx
The auxiliary equation of the differential equation is
2m2+12m+18=02(m2+6m+9)=0m2+6m+9=0(m+3)2=0m=3,3
Here roots are real and same
Therefore, the solution of the differential equation is
y=(c1+c2x)e3x

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