solving second order differential equation using ode45

so the equation is like y'' + (y^2 - 1)y' + y=0, with y'(0) = -1, y(0) = 0.1, and span of t is 0 to 30, step by 0.5, how do I initialized the point and using ode45 to solve the second order equation?

[Allen Li]

How do I change y'(0) to y(0)?

Answer 1

[Jan]

Convert the 2nd order equation into a set of 1st order equations:

dy(1) = y(2);
dy(2) = (1 - y(1)^2) * y(2) - y(1);

See: https://en.wikipedia.org/wiki/Ordinary_differential_equation#Reduction_to_a_first-order_system