In Problems 25-28 use (12) to verify that the indicated function is a solution of the given differential equation. Assume an appropriate interval I of definition of each solution. dy -3t e dt 25. x-3xy = 1; y = dx %3D

2. Find the general solution of the differential equation e-ty- y = 2e-t+e".

1. Determine by direct substitution whether or not the equation y =| x²-2x et +2x+2 is a solution to the differential equation y"-y"=xe". Make sure you answer the question in a complete sentence.

dy cosh(x), and dy = sinh(x). For this problem you may want to recall that if y = sinh(x), then dx dx2 It can be shown that y1 = sinh(2x), y2 = cosh(2x) and y3 e2x are solutions to the differential equation %3D xD³y - 9D²y – 4xDy+ 36y = 0 on (0, 0). What does the Wronskian of y1, y2, Y3 equal on (0, ∞)? W(y1, y2, Y3) = on (0, ∞0). Yes 1. Is {yı, Y2, Y3} a fundamental set for xD°y – 9D²y – 4×DY+ 36y = 0 on (0, ∞)?