y 1 = dsolve(' D2y+4 * Dy+29 * y = 0 '，' Dy(0)= 15 '，'？ y(0)=0 '，' x ')
y 1=(3*sin(5*x))/exp(2*x)
y2 = dsolve(' D2y-2 * Dy+5 * y = sin(2 * x)')
y2=sin(2*x)/5？ +? C5*cos(2*t)*exp(t)？ +? C6 * sine (2 * t)* experience (t)
For the third question, then we can't find a general solution, and we can only solve it by numerical solution. The numerical solution adopts the method of ode45 function, and the specific process is as follows:
Write the differential equation function that requires solution first, and open the editor:
% Write the function expression of the differential equation group to be solved!
Function? dy？ =? Stiffness (t, y)
dy？ =? Zero (3,1); %? Define array functions!
dy( 1)？ =? y(2)？ *? y(3)； % the first differential equation;
dy(2)？ =? -y( 1)？ *? y(3)； % second order differential equation;
dy(3)？ =? -0.5 1? *? y( 1)？ *? y(2)； % third order differential equation;
And save the function file with the default file name!
Write command line to solve differential equation;
Options? =? odeset('RelTol '， 1e-4，' AbsTol '，[ 1e-4？ 1e-4？ 1e-5])； The% definition solution option contains precision items!
[T，Y]？ =? Ode 45(@ Rigid, [0? 12],[0? 1? 1], option); % use ode45 to solve the equations, and save the solution results in the array T, Y!
Plot (t，y(:， 1)，' r-'，t，y(:，2)，' b-'，t，y(:，3)，' K.')% drawing！
Grid? Secondary% grid!
Run the above code to get the solution of the function:
Attach a picture!
Ask me questions! !