Observe that equation (3) has constant coefficients. If y1(x) and y2(x) form a fun- damental set of solutions of equation (3), show that y1(ln t) and y2(ln t) form a fundamental set of solutions of equation (2). Show that they are both solutions and also form a fundamental set.

The equations (2) and (3) you referred to are unavailable, but it is clear that you are trying to show that two set of solutions y1 and y2, to a (second-order) differential equation are solutions, and form a fundamental set. This will be explained.

SOLUTION OF A DIFFERENTIAL EQUATION.

Two functions y1 and y2 are set to be solutions to a differential equation if they both satisfy the said differential equation.

Suppose we have a differential equation

y'' + py' + qy = r

If y1 satisfies this differential equation, then

y1'' + py1' + qy1 = r

FUNDAMENTAL SET OF DIFFERENTIAL EQUATION.

Two functions y1 and y2 are said to form a fundamental set of solutions to a second-order differential equation if they are linearly independent. The functions are linearly independent if their Wronskian is different from zero.

If W(y1, y2) ≠ 0

Then solutions y1 and y2 form a fundamental set of the given differential equation.

i dont know sorry

step-by-step explanation:

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2