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anonymous
 5 years ago
I need to find the partivular solution to the differential equation dy/dx=(1+y)/x Given the initial conditon f(1)=1
anonymous
 5 years ago
I need to find the partivular solution to the differential equation dy/dx=(1+y)/x Given the initial conditon f(1)=1

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bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0I love diff equations! =) So first of all see if its separable

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0So separate it: \[dy/dx = (1+y)/x\]

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, I keep crashing on here but i will always reply: So multiply both sides by dx and divide both sides by 1+y

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0You will have: \[dy/(1+y) = dx/x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can't you think of it as dy/(1+y) you're in good hands later.

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0Integrate both sides: Left side will be just Ln1+y and the right side will be Lnx

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0So: Ln1+y = Lnx + C

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0Raise e to both sides to get rid of Ln: \[e^{Ln1+y} = e^{Lnx+C}\]

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0Rewrite and simplify: \[e^{Ln1+y} = e^{Lnx}*e^C\] \[1+y = Kx\]

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0(e to some constant is another constant so I just let that other constant be K) Now apply initial conditions: f(1)=1: 1+1 = 1K; 2 = K; K = 2

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0So your answer is: 1+y = 2x, or: y = 2x  1 <= Final answer

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0Im taking a differential equations course! IT IS FUN!! P.S.: Please click on become a fan if I helped, I really want to get to the next level!! Thanks =)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why do you multiply by e^c

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0there's a property: \[A^{B+C} = A^B * A^C\], so in our case: \[e^{Lnx+C} = e^{\lnx} * e^C\]

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0and e to some constant is another constant so I said let that constant be K. Any other questions?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no and thanks for your help
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