Question

dy/dx+4y=12 given that y(0)=2​

Answer 1

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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Answer 2

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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