Mikhail Kalmykov
Мастер
(1684)
4 года назад
xy'-y=-y^2(ln x+2)lnx
xy' - y = 9 -> y = C*x
x^2 C' =-C^2*x^2*ln(x)*(ln(x)+2)
-dC/C^2 = dx*ln(x)*ln(x) + 2*ln(x)*dx
1/C = x*ln(x)*ln(x) - 2*dx*ln(x) + 2*x*ln(x) - 2*dx
= x*ln(x)*ln(x)
1/y = 1/(x*C) = C1/x + ln(x)*ln(x)
1/y(1) = C1 = 1
1/y = 1/x + ln(x)*ln(x)
xy'-y=-y^2(ln x+2)lnx
-x*(1/y)' - 1/y = -(ln x+2)lnx
1/y = z
x*z' + z = (ln x+2)lnx
z = C/x
C' = (ln x+2)lnx
C = C1+x*ln(x)*ln(x)
Z =C1/x + ln(x)*ln(x)
1/y = C1/x + ln(x)*ln(x)
1/y(1) = C1 = 1
1/y = 1/x + ln(x)*ln(x)