- #1
shiri
- 85
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Find the particular solution of the differential equation
dy/dx = (3x+42y)/7x
satisfying the initial condition y(1) = 5.
Attempt:
dy/dx = 3/7 + 6y/x
dy/dx - 6y/x = 3/7
p(x) = -6/x
q(x) = 3/7
u(x) = -6 ∫(1/x)dx = -6ln|x|
e^(u(x)) = -x^6
1/e^(u(x)) ∫e^(u(x))q(x)dx
= 1/(-x^6) ∫(-x^6)(3/7)dx
= 3/(7(-x^6)) [(-x^7/7)+c]
=3x/49 - 3c/(7x^6)
y(1) = 5 = 3(1)/49 - 3c/(7(1)^6)
5 = 3/49 - 3c/7
242/49 = -3c/7
c = -242/21
So, what I got is
y(x) = 3x/49 + 242/(49x^6)
however, my professor said it's wrong. So, can anybody tell me what I did wrong? I'll be very appreciated. thanks.
dy/dx = (3x+42y)/7x
satisfying the initial condition y(1) = 5.
Attempt:
dy/dx = 3/7 + 6y/x
dy/dx - 6y/x = 3/7
p(x) = -6/x
q(x) = 3/7
u(x) = -6 ∫(1/x)dx = -6ln|x|
e^(u(x)) = -x^6
1/e^(u(x)) ∫e^(u(x))q(x)dx
= 1/(-x^6) ∫(-x^6)(3/7)dx
= 3/(7(-x^6)) [(-x^7/7)+c]
=3x/49 - 3c/(7x^6)
y(1) = 5 = 3(1)/49 - 3c/(7(1)^6)
5 = 3/49 - 3c/7
242/49 = -3c/7
c = -242/21
So, what I got is
y(x) = 3x/49 + 242/(49x^6)
however, my professor said it's wrong. So, can anybody tell me what I did wrong? I'll be very appreciated. thanks.