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i was using sympy to solve Differential eqs this was the code enter image description here

what does that C mean in the output and also is the answer right?Im new to solving D.E and im actually clueless where to start with

Noobishnoob
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  • The answer is right. If you are not familiar with the differential equations you cannot understand why an arbitrary constant C appears in the solution. Don't use a tool whitout knowing the intended use of the tool. – JJacquelin Oct 31 '20 at 15:36
  • you are right actually the teacher taught us about it but I quite actually didn"t get it so I was trying this way If i can get my head going – Noobishnoob Oct 31 '20 at 15:42

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The C1 is an arbitrary constant. It appears during the integration. Let's try to solve the equation. ($f(x) = y$ for simplicity)

$-5y+y'=2$

$\frac{dy}{dx}=2+5y$

$\frac{1}{2+5y}dy=dx$

Then we integrate both sides. Notice that an arbitrary constant will appear since the integration is not definite.

$\frac{1}{5}ln(5y+2)=x+C$

$5y+2=e^{5x+C}=e^{5x}e^C$

Since $e^C$ is a constant, we can substitute it with an arbitrary constant which is $C1$. You can try to solve for $y$ and you will get the result.

Michael Teguh Laksana
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