4x^2 y+8xy'+y=x, y(1)= 9, y'(1)=25
1 answer:
Answer with explanation:
--------------------------------------------------------Dividing both sides by 8 x
This Integration is of the form ⇒y'+p y=q,which is Linear differential equation.
Integrating Factor
Multiplying both sides by Integrating Factor
When , x=1, gives , y=9.
Evaluate the value of C and substitute in the equation 1.
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C+p=15
5c+7p=91
multiply 5 to 1st equation and subtract it from 2nd
multiply 5 to 1st equation to get
5c+5p=75
now subtract this from 2nd equation
thats 2p=16
so
p=8
now we find c from
c+p=15
c=7
Slope is -1/5
Y-intercept is 21
Equation is y=-1/5x+21
Yes it’s proportional :)
X/17y i think
I hope I helped!
The function rule is -1/5