Solve the differential equation. y' + 2y = 25

Annette Arroyo

Annette Arroyo

Answered question

2021-09-28

Solve the differential equation.
y' + 2y = 25

Answer & Explanation

faldduE

faldduE

Skilled2021-09-29Added 109 answers

Step 1
Given differential equation,
y'+2y=25...(1)
Step 2
Firstly evaluate the complementary function:
Auxiliary equation of given differential equation is,
m+2=0
m=−2
Since root are real and non repeated so complementary function is,
yc=ce2x
Step 3
Now evaluate particular integral:
So particular integral of given differential equation is,
yp=1D+2(25)
yp=1D+2(25e0x)
yp=25(1D+2e0x)
yp=25(10+2e0x)
yp=25(12e0x)
yp=252
Step 4
Since solution of differential equation is sum of complementary function and particular integral, so
y=yc+yp
y=ce2x+252
Step 5
Hence y=ce2x+252

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