- #1
Ready2GoXtr
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Problem:y' + y(1/x) = 3 x^2 y^2
Solution:p(x)= 1/x q(x) = 3x^2 <--- These are countinuous functions on the interval (0,+inf)
y^-2[y' + y(1/x) = 3 x^2 y^2] A
=> y'y^-2 + y^-1(1/x) = 3x^2
v = y^(-n+1) = y^-1 v' = -y^-2 y'
Plugin to problem A
v' + v/x = 3x^2 B
p(x) = 1/x q(x) =3x^2 <---- there's are continuous on the interval (0,+inf)
Find integral factor
h(x) = Int:[ 1/x dx] = ln(x) e^h(x) = e^(ln(x)) = x
multiply B through by factor
xv' + v = 3x^3
[xv]' = 3x^3
xv = Int:[3x^3 dx] = x^4 + C
solve for v
v = x^3 + C/x
replace v = y^-1
y^-1 = x^3 + C/x
y = (x^3 + C/x)^-1
Book listed solution = 2/(Cx - 3x^3)
Not sure what I am doing wrong there.
Solution:p(x)= 1/x q(x) = 3x^2 <--- These are countinuous functions on the interval (0,+inf)
y^-2[y' + y(1/x) = 3 x^2 y^2] A
=> y'y^-2 + y^-1(1/x) = 3x^2
v = y^(-n+1) = y^-1 v' = -y^-2 y'
Plugin to problem A
v' + v/x = 3x^2 B
p(x) = 1/x q(x) =3x^2 <---- there's are continuous on the interval (0,+inf)
Find integral factor
h(x) = Int:[ 1/x dx] = ln(x) e^h(x) = e^(ln(x)) = x
multiply B through by factor
xv' + v = 3x^3
[xv]' = 3x^3
xv = Int:[3x^3 dx] = x^4 + C
solve for v
v = x^3 + C/x
replace v = y^-1
y^-1 = x^3 + C/x
y = (x^3 + C/x)^-1
Book listed solution = 2/(Cx - 3x^3)
Not sure what I am doing wrong there.