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Mathematica Project #1 Due date: November 05, 2019 A hard copy of this assignment should not exceed 4 pages Kingston, 10/25/2019 1. Consider the homogeneous differential equation: dy $2y+2$y2 +y3 dst: _ m3 A (a) Find the general solution of this equation by using DSolve command. (1)) Use DSolve command to find the particular solutions of this equation that satises the initial conditions y(1) = 1 and y(1) = 2. ((2) Plot the obtained solutions on the interval [1, 2] on the same coordinate system. 2. Consider the linear differential equation: 3;\" + 4y' + 133; 2 62m sin(3;1:) + 3:4 + 11283: cos(3:). (a) Find the general solution of this equation by using DSolve command. (1)) Use DSolve command to nd the particular solutions of this equation that satises the initial conditions y(0) = .01,y'(0) = .02 and y(0) = 0,y'(0) = .01. (0) Plot the obtained solutions on the interval [0, 1] on the same coordinate system. 3. Consider the Euler's differential equation: $231\" 5my' + 93; = m4 + 21:3 lnm. (3) Find the general solution of this equation by using DSolve command