The function y1 = x^2 is a solution of (x)^2 Solution x2 - 3xy\' + 4y = 0 3xy\' - 4y = x2 y\' - (4/3x)y = x/3 Integrating factor = e^[integration of (-4/3x)] = x-4/3 multiply the integrating factor to the equation, we get x-4/3y\' - (4/3)x-7/3y = x-1/3/3 d(x-4/3y)/dx = x-1/3/3 x-4/3y = [x2/3]/2 + C.

1. The function y1 = x^2 is a solution of (x)^2
Solution
x2 - 3xy' + 4y = 0
3xy' - 4y = x2
y' - (4/3x)y = x/3
Integrating factor = e^[integration of (-4/3x)] = x-4/3
multiply the integrating factor to the equation, we get
x-4/3y' - (4/3)x-7/3y = x-1/3/3
d(x-4/3y)/dx = x-1/3/3
x-4/3y = [x2/3]/2 + C