Solve a second order differential equation in matlab?

I have to solve the equation d2y/dx2+.5dy/dx+7y=0 with initial conditions y(0)=4 y'(0)=0 with x ranging from 0 to 5 with a step size of .5. How do I go about doing this?

Answer 1

[Azzi Abdelmalek]

You can transform your equation d2y/dx2=.-5dy/dx-7y to get:

y1=y
y2=dy/dx

dy1=dy/dx=y2
dy2=d2y/d2x=-5dy/dx-7y=-5y2-7y1

Create a file named myode.m

function dy=myode(x,y)
dy=[0;0]
dy(1)=y(2)
dy(2)=-5*y(2)-7*y(1)

Then run these lines

yin=[0 4 ]  % initial values
time=[0 5]
[x,y]=ode45(@myode,time,yin)
plot(x,y)

Answer 2

[Jaisai Pranav Yannam]

y''+16y=2 cos^2x,y(0)=0,y'(0)=1

Answer 3

[Ritu Rani]