a)
The functions y1 = x^2 and y2 = x^5 aretwo solutions of the equation
x^2 y ? ? 6 x y ? + 10 y = 0.
Let y be the solution of the equation x^2 y ? ? 6 x y? + 10 y = 3 x^5
satisfyng the conditions y ( 1 ) = 0 and y ? ( 1 ) =1.
Find the value of the function f ( x ) = y ( x ) / ln?( x ) at x = 2.
b)
The function y1 = x^5 is a solution of theequation
x^2 y ? ? 11 x y ? + 35 y = 0.
Let y2 be the solution of this equationsatisfying the conditions
y2 ( 1 ) = 0 and y2 ? ( 1 ) = 2.
Find the value of y2 at x = 2.
c )
The function y1 = x^7 is a solution of theequation
x^2 y ? ? 8 x y ? + 14 y = 0.
Let y2 be the solution of this equationsatisfying the conditions
y2 ( 1 ) = 1 and y2 ? ( 1 ) = 2.
Find the value of y2 at x = 2.
