How can I solve this second order equation?

 if f=60 and k=0.105with plot the relationship between qf and fo?See the image

[Shada ahmed]

Fo^2_(2*f*k)/Qf*(pi-2*k*f)*fo-f^2=0

Answer 1

[AMIT POTE]

Hi Shada,

Seecond order differential equations can be solved using dsolve() or ode45() function. You can go through the following documentation for better understanding

https://www.mathworks.com/help/symbolic/dsolve.html

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

[Sam Chak]

@AMIT POTE

It is impossible to solve the given equation because it is not a differential equation to begin with

Fo^2_(2*f*k)/Qf*(pi-2*k*f)*fo-f^2=0

There are Fo, f, k, Qf, pi, and another fo, with Fo, Qf, and fo are unknowns.

Furthermore, the underscore symbol in Fo^2_ is not intelligible from the mathematical notation perspective.

Most likely @Shada ahmed refers the "second order" to the polynomial order in the equation.

Answer 2

[Sam Chak]

@Shada ahmed

This is not exactly the equation given, but it should give you the idea of ''visualizing' the relationship between Fo and Qf.

f = 60;
k = 0.105;
fimplicit(@(Fo, Qf) (Fo.^2) + (2*f*k)./Qf*(pi-2*k*f).*Fo - f^2, [-0.1 0.1 -4e-3 4e-3])
grid on
xlabel('Fo')
ylabel('Qf')