Description
#1.Write and then solve for y = f(x) the differential equation for the statemen "The rate of change of y with respect to x is inversely proportional to y^4." #2.Solve the differential equation for y = f(x) with the condition y(1) = 1.
Explanation & Answer
Rate of change = dy/dx
Equation: dy/dx = A/y^4 where A is an unknown proportionality constant.
Solving the diff. equation: y^4*dy=A*dx integrating: y^5/5=Ax+B, B is another constant relating to initial condition that do not affect the rate of change.
put y=1 at x=1 we get 1/5 =A+B. or:
y^5/5=Ax + 1/5-A or y^5=5A(x+1)-5 or y= 5th root[(5A(x+1)-5]
We cannot determine A completely unless we have one more data point. For example, if we are given also that y(0)=0 we can solve for A, B : B= 0 , A = 1/5.
Review
Review
24/7 Homework Help
Stuck on a homework question? Our verified tutors can answer all questions, from basic math to advanced rocket science!
Similar Content
Related Tags
To the Lighthouse
by Virginia Woolf
All Quiet on the Western Front
by Erich Maria Remarque
Unf*ck Yourself
by Gary John Bishop
Steppenwolf
by Hermann Hesse
The Adventures of Huckleberry Finn
by Mark Twain
Principles - Life and Work
by Ray Dalio
The Catcher in the Rye
by J. D. Salinger
2001 A Space Odyssey
by Arthur Clarke