Differential equation of second order with two variables
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to be solved is the equation ๐ธ๐ผ๐ค4(๐ฅ,๐ก)+๐ ๐คฬ(๐ฅ,๐ก)=0 and this can be solved by expressing ๐ค(๐ฅ,๐ก)= ๐(๐ฅ)โ
๐(๐ก)
for ๐(๐ฅ) we do have this expression ๐๐(๐ฅ)=๐ดโ
[sin(๐๐ ๐ฅ๐ฟ)โsinh(๐๐ ๐ฅ๐ฟ)+sin(๐๐)+sinh(๐๐)cos(๐๐)+cosh(๐๐)โ
(cosh(๐๐ ๐ฅ๐ฟ)โcos(๐๐๐ฅ๐ฟ)) ]
and for ๐๐(๐ก)=๐(0)cos(๐๐ ๐ก)+๐ฬ(0)๐sin(๐๐(๐ก))=๐ถ(0)โ
๐๐๐ (๐๐ ๐ก+๐(0)). Whereas ๐๐ is solved through this equation 1+cos(๐๐)โ
cosh(๐๐)=0
I am guessing that to solve the first differential equation as conditions we can use the three other equations given.
Does anyone has some tipps how this differential equation can be solved?
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Pranjal Saxena
il 28 Lug 2023
Hi Florian,
I understand that you want to solve this second order differential equation.
You can use the โSymbolic Math Toolboxโ in MATLAB to do so.
A typical approach to solving higher-order ordinary differential equations is to convert them to systems of first-order differential equations, and then solve those systems.
First you need to convert the second-order differential equation into a system of differential equations that can be solved using the numerical solver โode45โ of MATLAB.
You can refer to the following MATLAB documentations for more information:
I hope this helps.
Warm Regards,
Pranjal.
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