1st order differential equation , boundary conditions

please can someone help me to solve this 1st differential equation my function is Dp=kp ln(450/p) p(0)=40 and p(15)=95 , k is constant can someone help please, i am new to MATLAB k is constant and p is p(t)

Answer 1

[Torsten]

syms y1(t) y2(t)
eqn = [diff(y1,t) == y2*y1*log(450/y1), diff(y2,t) == 0];
cond = [y1(0)==40, y1(15)==95];
[y1Sol(t) y2Sol(t)] = dsolve(eqn,cond)

[Torsten]

from Takey Asaad:

can you plot it and find value at t=15 and t=0?

[Torsten]

y1Sol(0)
y1Sol(15)
fplot(y1Sol)

Answer 2

[Takey Asaad]

ans =

40

ans =

450*exp(exp(20*log(log(19/90)) - 19*log(log(4/45))))

answer at t=300 must be 450 and the plot is empty , do you know what is the problem. Thanks,

Answer 3

[Takey Asaad]

Hi, why you use log instead of exp?

[Torsten]

Because you use "ln" in your problem formulation.

And please do not always create answers in this thread. The replies you give are comments to answers.

What do you get for y1Sol ?

Best wishes

Torsten.