anonymous
  • anonymous
Could someone help me with this problem , please
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
IrishBoy123
  • IrishBoy123
2nd order non-hom D.E.: you will need particular solution and complementary solution so for complementary solution, first solve: \(m\ddot x + b \ \dot x = 0\) or \(\ddot x + \frac{b}{m} \ \dot x = 0\) using diff operators: \(D(D+\frac{b}{m}) x = 0 \) so you should get a constant, \(c_1\), and constant \(c_2\) times an exponential \(e^{-bt/m}\) for the particular solution, start with \(x(t) = A t^2 + Bt + C\) and you get \(\dot x = 2 A t + B\) and \(\ddot x = 2A\) then stuff these back into \(\ddot x + \frac{b}{m} \ \dot x = g\) to find A, B and C then add them up and apply the boundary conditions, \(x(0) = 0\) and \(\dot x(+\infty) = 0\) to find the \(c_1\) and \(c_2\). those are the steps.
Astrophysics
  • Astrophysics
Ah very nice @IrishBoy123

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