Consider the initial value problem ´t (t − 2) y' + cos(t) y = t − 2 ly(3): = 4 The largest open interval where the solution of the initial value problem is guaranteed to be defined is (2, +00) (0, +∞0) (0,2) (2,4) (π/2, +00) Classify each of the following first order differential equations 1. is a linear equation 2. is a separable equation is a (x + 1) y' + (x + y)² = x² xy (2 - 2/2) dz + 2 / dy = 0 + y² 3. In(y) 1+ ln(x) dx + dy = 0 homogeneous In(x) In(y) equation is a Bernoulli 4. equation (12² + cos(y)) d བ is an exact equation 5. + cos(y) dx + (2 y ln(x) − x sin(y)) dy = 0 - (x³ y² + x e³) (y' + xy + 1) − ye³ − x² y³ = 0 -