How can i make a code to find y of y''=y*y' ?

(sorry about my english skill)

i want to know how can i make a ode code.

if i have y'=2y then i can make a code like

[T,Y] = ode45(@(t,y) 2*y,[0 1],1); plot(T,Y);

but if i have y''=y*y' , i can't make a code

help me (T_T)

Answer 1

[Roger Stafford]

To solve your equation numerically using one of the ode functions, you set it up as two simultaneous differential equations:

   dy(1) = y(2)
   dy(2) = y(1)*y(2)

See:

   http://www.mathworks.com/help/matlab/ref/ode45.html

for some examples of this.

However, it should be noted that the ordinary methods of calculus can be used to solve this particular differential equation. Its solutions are:

   y = 2*a*tan(a*t+b)
   y = -2/(t+b)
   y = -2*a*coth(a*t+b)
   y = b
   y = -2*a*tanh(a*t+b)

where a and b are arbitrary constants. (Corrected twice)

[Roger Stafford]

I have added two more solution formulas involving the hyperbolic cotangent function and a reciprocal formula.