Asked by Danielle
How do you find the primes denote derivatives with respect to x. Such as xy'+ 5y= 7x^2, y(2)= 5
Answers
Answered by
drwls
Rewrite as
dy/dx + (5/x)*y = 7x
That is a first-order linear D.E. that can be solved using the method of integrating factors. In this case,
let P(x) = 5/x and Q(x) = 7x
Find the "integrating factor"
r(x) = exp(P dx) = 5 lnx
The solution is then
r(x)*y = integral of r*Q dx + C
Then use the y(2) = 5 information to compute C
dy/dx + (5/x)*y = 7x
That is a first-order linear D.E. that can be solved using the method of integrating factors. In this case,
let P(x) = 5/x and Q(x) = 7x
Find the "integrating factor"
r(x) = exp(P dx) = 5 lnx
The solution is then
r(x)*y = integral of r*Q dx + C
Then use the y(2) = 5 information to compute C
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