a) Solve the differential equation: (x+1)\frac{dy}{dx}-3y=(x+1)^4 given that y=16ZS

Cian Orr

Cian Orr

Answered question


a) Solve the differential equation:
given that y=16 and x=1, expressing the answer in the form of y=f(x).
b) Hence find the area enclosed by the graphs y=f(x), y=(1x)4 and the xaξs.
I have found the answer to part a) using the first order linear differential equation method and the answer to part a) is: y=(1+x)4. However how would you calculate the area between the two graphs (y=(1x)4 and y=(1+x)4) and the x-axis.

Answer & Explanation

Jocelyn Harwood

Jocelyn Harwood

Beginner2022-02-19Added 8 answers

Good job on solving part (a) of the question. That was the tough part. Part (b) is much more easier.
As you stated, we get that the function is:
Now, in order to find the area between this function, the function f(x)=(1x)4, and the x-axis, we need to the find intersection points:
When x=0, (0+1)4=(01)4=1.Thus, we get that the two functions intersect at the point (0,1).
Next, we look at where each of the two functions intersect the x-axis. We get that:
Therefore, we get our two endpoints: (-1,0) and (1,0).
Thus, we can use construct our integral now:
Hope that helped. Comment if you have any questions.

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