Find intersection point between u(t) = t^2(t-1) and u = 10.

Hello, I did dsolve differential equation. But I don't know how to find intersection point values between Root differential equation and u = 10.

syms u(t)
ode = t*diff(u,t) == t^2 + 3*u
condition = u(2) == 4;
uSol(t) = dsolve(ode, condition)
ezplot(uSol)
hold on
grid on
% try to plot u == 10
t_ = 0:4;
plot(t_, ones(size(t_)) * 10)

How can I find intersection point values of uSol and u == 10?

Thank you!

Answer 1

[Stephan]

Simply use the function you calculated:

>> t_sol = vpasolve(uSol == 10,t)
 
ans =
 
                                         2.5445115283879060011505370208062
 - 0.77225576419395300057526851040312 + 1.8258281475484665736721861577551i
 - 0.77225576419395300057526851040312 - 1.8258281475484665736721861577551i

I think you can withdraw the complex solutions and the result looks like in would work looking at the plot. Testing the solution:

 >> test_sol = uSol(t_sol(1))
 
test_sol =
 
10.0

[Lam Phucnghi]

Thank you very much!