# How do I solve an ODE of the form y'=ay^3 +by^2 +cy +d?

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Gabriel Baranoski on 25 Jan 2022
Commented: Jon on 26 Jan 2022
I have a vector, for example "pn" of size (20,1). Each point of data describes a coeffecient of y to the power of 20 minus that data point indices (made from the polyfit function in matlab).
For example, pn(15,1) = 5 translates to 5y^5
This defines a large polynomial which looks similar to the title example.
I know that the ODE I have is of the form y'=ay^19 + by^18 +cy^17 +...+gy +h
how can i solve this ode to make a plot of y as a function of t?
I know about the ODE functions like ode45 etc, but I'm not sure how to use them with my ode form.
Thanks!
James Tursa on 25 Jan 2022
Can you verify that the form has y's in the polynomial and not x's or t's? And do you have numeric initial conditions?

Jon on 25 Jan 2022
The ode solvers, e.g. ode45 require a function handle which will evaluate the current value of the derivative given the current state. So define your function for example as:
fun = @(y)polyval(pn,y)

Gabriel Baranoski on 26 Jan 2022
Hey so I ended up figuring it out. This is my code to solve the ODE below:
FK=polyfit(MFPs(:,1),MFPs(:,2),20);
tspan = [0 :0.05:50];
x0 = 0;
[t,v]=ode45(@(t,v) ((FK(1)*v^20) + (FK(2)*v^19) + (FK(3)*v^18) + (FK(4)*v^17) + (FK(5)*v^16) + (FK(6)*v^15) + (FK(7)*v^14) + (FK(8)*v^13) + (FK(9)*v^12) + (FK(10)*v^11) + (FK(11)*v^10) + (FK(12)*v^9) + (FK(13)*v^8) + (FK(14)*v^7) + (FK(15)*v^6) + (FK(16)*v^5) + (FK(17)*v^4) + (FK(18)*v^3) + (FK(19)*v^2) + (FK(20)*v) + (FK(21)) - FR - (Y*(v^2)))/M ,tspan,x0);
plot (app.UIAxes,t,v*3.6);
There are a few terms included there that change the ODE from how i originally stated, but this solves the ode accurately.
Maybe theres a way to reduce the ode solve command but I'm not to sure how.
Jon on 26 Jan 2022

R2021b

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