GHS 554 Partial Differential Equations Assignment #1 (Problems from Chapter 1 of the Textbook) 1. Find the Ge#er/ So/wfz.o# to the First Order differential Equation (2x2y + x)y' + (2xy2 + y + 3x2) = 0 Having found the General Solution, find the solution that satisfies the initial condition y(1) = 1. 2. Find the General Solution to x2y, + 4ry + 3 - 0 Having found the Gc#er/ So/zffz.o#, find the solution that satisfies \ y(1) - 1. 3. Verify that yi = e-I is a solution to the second order linear differential equation 2y" + 3y, + y - 0 Use equation (1.2.10) to construct a second independent solution and, thus, the general solution that involves two arbitrary constants of integration. Now, apply the initial conditions y(0) = 0 and y'(0) = 1 and find the solution satisfying them. 4. Construct the General Solution to 2y,, + 3y, + y - 4x + 1 Apply the initial conditions y(0) = 0 and y'(0) = 1 to this solution