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Question: How do I simplify a complex equation as a solution to a differential equation?

Question:How do I simplify a complex equation as a solution to a differential equation?

Mathrookie94 20 Maple
simplify simplification differential-equations
May 23 2024
1

Hello :) 

I don't know how to further simplify a complex equation as a solution to a differential equation. I have already tried "simplify(%)" etc. but it only repeats the same equation. I also know that it can be simplified to a much more "nice" equation in WordMat and TI-Nspire. I have attached a screenshot of my work. 

Thank you! 

with(Gym)

with(plots)

with(DEtools)

 

I need to find the solution to the differential equation: y'=0.0768*f(x)^2/3-0.0102*f(x) when f(1)=59. 

 

dsolve({diff(f(x), x) = 0.768e-1*f(x)^(2/3)-0.102e-1*f(x), f(1) = 59}, f(x))

f(x) = 2097152/4913+(384/4913)*(16384-4352*59^(1/3)+289*59^(2/3))*exp(17/2500-(17/2500)*x)+(1/4913)*(835584*59^(1/3)-110976*59^(2/3)-1807285)*exp(51/5000-(51/5000)*x)+(49152/4913)*(17*59^(1/3)-128)*exp(17/5000-(17/5000)*x)

 (1)

simplify(%)

f(x) = 2097152/4913+(384/4913)*(16384-4352*59^(1/3)+289*59^(2/3))*exp(17/2500-(17/2500)*x)+(1/4913)*(835584*59^(1/3)-110976*59^(2/3)-1807285)*exp(51/5000-(51/5000)*x)+(49152/4913)*(17*59^(1/3)-128)*exp(17/5000-(17/5000)*x)

 (2)

 

Download worksheet_.mw
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