Determine all solutions to the differential equation y′′−2y′−15y = 0 of the form

preprekomW

preprekomW

Answered question

2021-09-20

Determine all solutions to the differential equation y′′−2y′−15y = 0 of the form y(x)=erx, wherer is a constant. Use your solutions to determine the general solution to the differential equation.

Answer & Explanation

pivonie8

pivonie8

Skilled2021-09-21Added 91 answers

Step 1
The given differential equation is, y−2y′−15y=0.
Solve the given homogeneous differential equation.
m22m15=0
m25m+3m15=0
m(m-5)+3(m-5)=0
(m+3)(m-5)=0
m=-3,5
Thus, the general solution is of the form y=c1e3x+c2e5x.
Step 2
The required solution is, y=c1e3x+c2e5x.

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