a)
Find the value of the Wronskian of the functions f =x^7
and g = x^8 at the piont x = 1.
b)
Let y be the solution of the equation y ? ? 5 y ? + 6y = 0
satisfying the conditions y ( 0 ) = 1 and y ? ( 0 ) = 2.
Find ln ? ( y ( 1 ) ).
c)
Let y be the solution of the equation y ? + 2 y ? + 2y = 0
satisfying the conditions y ( 0 ) = 0 and y ? ( 0 ) =1.
Find the value of y at x = ?.
d)
Let y be the solution of the equation y ? + 6 y ? + 9y = 0
satisfying the conditions y ( 0 ) = 0 and y ? ( 0 ) =1.
Find the value of the function f ( x ) = ln [(y(x))/(x)] at x = 1.
e)
One of solutions of the equation y ? ? y ? + y = x^2 + 3x +5
is a function of the form y = A*x^2 + B*x + C.
Find the value of the coefficient C.
f)
One of solutions of the equation y ? ? 2 y ? + 2 y = ( x + 1 )e^x
is a function of the form y = ( A*x + B ) e^x.
Find the value of the coefficient B.
