Economy, asked by ridiprahang, 3 months ago

dy/dx+4y=12 given that y(0)=2​

Answers

Answered by madhumani9
2

Answer:

Substituting the value

d×2/dx+ 4×2=12

2d/dx+8=12

2d/dx=12-8

2d/dx=4

d/dx=4/2

simplify

d/dx=2

simplify d and d cancelled

so X=2

Explanation:

X=2 is the answer bro

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Answered by rinayjainsl
1

Answer:

The solution of the differential equation is

y=3+e^{-4x}

Explanation:

The given differential equation is \frac{dy}{dx}+4y=12 and it is also given that

y(0)=2

We are required to find the solution of the given differential equation which is done as shown below

\frac{dy}{dx}+4y=12\\= > \frac{dy}{dx}=12-4y=-4(y-3)\\= > \frac{1}{y-3}dy=-4dx

Integrating on both sides we get

\int \frac{1}{y-3}dy=\int(-4dx)\\= > ln|y-3|=-4x+c

We know that y(0)=2 hence x=0= > y=2 substituting this in above relation we get

ln|2-3|=0+c= > ln1=c\\= > c=0

Hence the solution becomes

ln|y-3|=-4x\\= > y=3+e^{-4x}

Therefore,

The solution of the differential equation is

y=3+e^{-4x}

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