3. Suppose a second order linear homogeneous equation y" + P(x)y' + Q(x)y = 0 has the following two solutions: Y1(x) = cos(x) + 5 sin(x), Y2(x) = e* sin(3x). a) Use Wrońskian determinent to decide whether y₁ and y2 are linearly independent. b) Find the solutions with the following initial conditions. i) y(0) = 1, y'(0) = 0 ii) y(0) = 0, y'(0) = 1 iii) y(0) = 22, y'(0) = 33

Suppose that Y1 and y2 are distinct particular solutions to y" + p(t)y' + q(t)y = 2 cos(t). Which of the following would be another particular solution to this equation? O y1 – Y2 Y1 + Y2 O 2yı + Y2 Зу1 — 2у2 - О Зул + Зу2

find the general solution of y''+y=cos(t) using the undetermined coefficients method

Suppose we want to create something with a particular behavior. In eachpart below, find a second order, linear, constant coefficient, homogeneousdifferential equation with this y(t) as its general solution. y(t) = c1(e^3t)sin(2t) + c2(e^3t)cos(2t)