The general solution of the differential equationy^{n}-9y=0can b

Harlen Pritchard 2021-09-16 Answered

The general solution of the differential equation
yn9y=0
can be written in the form
y(x)=Aem1x+Bem2x,
where A,B,m1,m2R and m1>m2.
a) Solve the auxiliary equation, and enter the values of m1 and m2 in the boxes.
Do not enter decimals in your answers. Enter whole numbers, fractions or square roots as appropriate.
If you need to enter a square root, e.g. x, enter this as x.
m1= ?
m2= ?

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Expert Answer

aprovard
Answered 2021-09-17 Author has 94 answers

Step 1: To Find
We have to find the general solution of the differential equation y9y=0 and write it in the form of y(x)=Aem1x+Bem2x.
Step 2: Calculation
y9y=0
Auxilary Equation: m29=0
m232=0
(m+3)(m3)=0
m=3,3
Since roots of the auxiliary equation are distinct and 3<3, then the solution is
y(x)=Ae3x+Be3x
Hence m1=3 and m2=3.

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