Find the general solution of the following equation. u'(t)+12u=15

Kye

Kye

Answered question

2021-09-12

Find the general solution of the following equation.
u(t)+12u=15

Answer & Explanation

Clara Reese

Clara Reese

Skilled2021-09-13Added 120 answers

Step 1
The given first-order linear equation is u'(t)+12u=15.
Step 2
Find the general solution of u'(t)+12u=15.
dudt+12u=15
dudt=1512u
dudt=3(54u)
du(54u)=3dt
Step 3
Integrate on both sides,
du(54u)=3dt
14ln(54u)=3t+C
ln(54u)=12t4C
(54u)=e124C
4u=e12tC1+5
u=e12tC14+54
Hence, the general solution of the first-order linear equation is u(t)=e12tC14+54.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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