Homework SourseConsider the differential equation dydx 13 xxy7 where x 0
Consider the differential equation [dy/dx] = [(13 + x)/(xy^7)], where x > 0.
Find the solution to the differential equation when y(1) = 2 in the form
y8 =
Find the solution to the differential equation when y(1) = 2 in the form
y8 =
Solution
Consider the differential equation [dy/dx] = [(13 + x)/(xy^7)],
dy/dx = (13+x)/x y^7
y^7 dy = (13+x)/x dx = (13/x + 1) dx
take integration
y^8/8 = 13lnx + x +C
y^8 = 8 ( 13lnx + x +C)
y(1) =2
2^8 = 8 ( 13 ln1 + 1 + C)
256 = 8(C+1)
32 = C+1
C = 32-1 = 31
y^8 = 8 ( 13lnx + x +31)
![Consider the differential equation [dy/dx] = [(13 + x)/(xy^7)], where x > 0. Find the solution to the differential equation when y(1) = 2 in the form y8 =Sol](/WebImages/28/consider-the-differential-equation-dydx-13-xxy7-where-x-0-1076273-1761564537-0.webp "Consider the differential equation [dy/dx] = [(13 + x)/(xy^7)], where x > 0. Find the solution to the differential equation when y(1) = 2 in the form y8 =Sol")
