MATLAB can solve differential equations using the dsolve command. dsolve symbolic solution of ordinary differential equations. Example: syms y(x) Dy(x) = diff(y) D2y(x) = diff(y, 2) YGS1 = dsolve (D2y+2Dy+y==0) YGS2 = dsolve (D2y+2Dy+y==0, y(0)=-1, y(0)==2) Problems: Solve the following differential equations, using the initial conditions when applicable 1. y" + 8y + 16y = 0, y(0) = 1, y (0) = 0 2. y2"-3y + 2y2 = 0, y2(1) = 1, y(1) = 4 3. y3"+8y + 17y3 = 0 4. y + 8y +16y4=0 5. y-729ys=0 Script 1 %Solve the given Homogeneous Differential Equations with Constant Coefficients 2 %Initialize the variables 3 4 5 %Solve the equation y"+8y'+16y=0, y(0)=1, y'(0)=0. Save your answer as y1; 6 7 %Solve the equation y"-3y+2y=0, y_2(1)=1, y_2(1)=4. Save your answer as y2; 8 9 %Solve the equation y"+8y'+17y=0. Save your answer as y3; 10 11 %Solve the equation y^{IV} + 8y" + 16y=0. Save your answer as y4; 12 13 %Solve the equation y^{VI}-729y=0. Save your answer as y1; Save C Reset MATLAB Documentation