Answer Happy

Question 1 Solve the following separable differential equations. If an initial condition is given, find an explicit particular solution to the IVP. Otherwise, find an explicit general solution. (Your solutions should not be in quadratures.) 1. dx dt 2. y'(x) 3. du dT 2. + = 3. x x (you can assume that t > 0) t dw dx 3x² ex 2y - 5 Question 2 Solve the following differential equations by using an integrating factor. If an initial condition is given, find an explicit particular solution. Otherwise, find an explicit general solution. 1. x' (t) + 3x = t+e=2t dy 1 dt with y(0) u² - 27u² with u(0) = - 2 :3 cos (2t) 74 =₁ = 1 Question 3 + (x + 1)w = x with w(ln(2)) = 1