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Question
If dy/dx = x^3 y^2 and x=2 when y=-1 then y=f(x) is?
This is a separable differential equation.
dy/dx = x^3 y^2
y^-2 dy = x^3 dx
Integrate the left with respect to y and the right with respect to x and get
-y^-1 = x^4/4 + c
so
y = -1/(x^4/4 + c)
when x=2 , y=-1 , so substitute these values for x and y and solve for c
-1 = -1/(2^4/4 + c)
-1 = -1/(4 + c)
1 = 1/(4+c)
4+c = 1
c = -3
We now have the solution,
y = -1/(x^4/4 - 3)
(You can check that this solution is correct by finding the derivative)
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| Comment | Thank you very much for all the help you have given me. Socrates is very knowledgeable and explained how to compute my problem with great understanding. I hope you can help me in the future. Thank you once again for your time and consideration! | ||
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Calculus
Answers by Expert:
Socrates
Expertise
I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.
Experience
Ph.D. in Mathematics and many years teaching Calculus at state universities.
Education/Credentials
B.S. , M.S. , Ph.D.
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