%% SOLVING A HIGHER ORDER INITIAL VALUE PROBLEM %% % Here is an example of how you can use MATLAB to solve an initial value % problem. %% % Section 4.2 #31 % % Find the solution of the inital value problem % % $$y^{iv} \mbox{--} 4 y''' + 4 y'' = 0,\quad y(1)=\mbox{--}1,\ y'(1)=2,\ y''(1)=0,\ y'''(1)=0$$ % % and plot its graph. How does the solution behave as _t_ tends to infinity? %% % Here are the equation and initial conditions. eqn = 'D4y - 4*D3y + 4*D2y = 0' ic = 'y(1) = -1, Dy(1)=2, D2y(1)=0, D3y(1)=0' %% % I use *dsolve* to solve the problem. This time, I give it a second % argument, the initial conditions. I also tell *dsolve* what % the independent variable is. If the equation only involves one variable, % this isn't essential. If the equation involves more than one and you % want to think of the others as parameters, it is essential to tell MATLAB % which is the independent variable. sol = dsolve(eqn,ic,'t') %% % I'll use *ezplot* to plot the solution. (Of course this one is easy to % plot by hand.) ezplot(sol) %% % The solution tends to infinity as _t_ tends to infinity - it grows linearly.