MATLAB can solve differential equations using the dsolve command. dsolve symbolic solution of ordinary differential equations. Example: syms y(x) Dy (x) = diff(y) Dzy (x) - diff(y,2) YGS1 = dsolve(D2y+2*Dy+y==®) yGs2 - dsolve(02y+2*Dy+y==®, y(@)==1, y(@)==2) Problems: solve the following differential equations, using the initial conditions when applicable 1. yı"+ 8y, + 16y) = 0, yı (0) = 1, y,(0) = 0 2. yz" – 3y, + 2y2 = 0, y2( 1) = 1, y,(1) = 4 3. y"+ 8y, + 17y) = o 4. y + 8y! + 16y4 = 0 5. y – 729ys = 0 Script e A Save CReset MATLAB Documen 1 Xsolve the given Homogeneous Differential Equations with constant Coefficients 2 XInitialize the variables 4 5 Xsolve the equation y"+8y'+16y=0, y(e)=1, y'(@)=e. save your answer as y1; 7 Xsolve the equation y"-3y'+2y=0, y_2(1)=1, y_2'(1)=4. save your answer as y2; 9 X5olve the equation y"+8y'+17y=e. Save your answer as y3; 10 11 Xsolve the equation y^{IV} + 8y" + 16y=e. Save your answer as y4; 12 13 XSolve the equation y^{VI}-729y=e. Save your answer as y1;