Show all your work in the space provided under each question. Please write neatly and present your answers in an organized way: find the general solution of the di erential equation: y . 2xy = x: solve. x + x = 1 + (t) x(0) = 1 x (0) = 0. Page 2: find the general solution. y = x + 1 y4 + 1. Page 3: find the general solution. x2y + 3xy + 5y = 0. Page 4: find two linearly independent power series solutions to the di erential equation. Include at least 3 nonzero terms in each series. What is the radius: find the taylor series about x = 1 for g(x) = x2 + 1 . What is the radius of convergence of this series: a mass of 1 kg is attached to a spring with spring constant 2 kg/sec2 . This system is damped with a shock absorber which has damping constant 3 kg/sec .
