Linear Differential Equations in Kinematics

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In summary, the conversation discusses solving a system of linear differential equations in kinematics involving gravity and air resistance. The equations are written in terms of velocity and a substitution is used to solve the second equation, which involves a complicated integral. The conversation also includes a debate about whether the initial equation is correct and the difference between using magnitude and vector notation.
  • #36
Well, but I don't have so much experience in seprating fractions :'(. How do you seprate the fraction
[tex] \frac{1}{1\pm u} [/tex]
 
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  • #37
P3X-018 said:
Well, but I don't have so much experience in seprating fractions :'(. How do you seprate the fraction
[tex] \frac{1}{1\pm u} [/tex]
Those can't be decomposed further, but:
[tex]\frac{1}{1-u^{2}}=\frac{1}{2}(\frac{1}{1+u}+\frac{1}{1-u})[/tex]
[tex]\frac{1}{1+u^{2}}[/tex] cannot be partially fractiondecomposed in real partial fractions.
 
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