Determine the order of each differential equation, and whether or not the given functions are solutions of that equa- tion.
(a) (y)²=4y: y1(x) = x², y2(x) = 2x², уз (х) = e⁻ˣ
(b) 2yy' = 9 sin 2x; y1(x) = sinx, y2(x) = 3 sin x, y3(x) = eˣ
(c) y"-9y = 0; y1(x)=e³ˣ - eˣ, y2(x) = 3 sinh 32,
y3 (x) = 2e³ˣ - e⁻³ˣ
(d) (y')²-4xy'+4y=0; y1 (x) = x²-x, y2(x) = 2x-1
(e) y" + 9y = 0; y1 (x) = 4 sin 3x + 3 cos 3x,
y2 (x) = 6 sin (3x + 2)
(f) y"-y'-2y = 6; y1(x)=5e²ˣ-3, у2 (х) = -2e⁻ˣ-3
(g) y'"-6y" + 12y'- 8y = 32 - 16x;
y1(x) = 2x - 1+(A+Bx + Cx²) e²ˣ for any constants A, B, C
(h) y' + 2xy = 1; y1(x) = Ae-² ∫₀ˣeᵗ² dt,
y2(x) = e⁻ˣ²∫ₐˣeᵗ² dt, for any constants A and a.