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undetermined coefficients in solving ODE question

Posted 8 years ago
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Hi, these guys have a question I too need to solve. If u can do it I will appreciate it. undetermined coefficients

POSTED BY: jerryan samba
Posted 8 years ago

I am not sure I read yr equation correctly (better to insert Mathematica code). But this is what DSolve gives you:

In[201]:= DSolve[y''[x] + 6 y[x] == -294 x^2 Exp[6 x], y[x], x]

Out[201]= {{y[x] -> 
   C[1] Cos[Sqrt[6] x] + C[2] Sin[Sqrt[6] x] - 
    1/21 E^(6 x) (17 - 84 x + 147 x^2) (Cos[Sqrt[6] x]^2 + 
       Sin[Sqrt[6] x]^2)}}

Which is indeed the answer you propose:

In[208]:= -(1/21) E^(6 x) (17 - 84 x + 147 x^2) + 
   C[1] Cos[Sqrt[6] x] + C[2] Sin[Sqrt[6] x] == 
  C[1] Cos[Sqrt[6] x] + C[2] Sin[Sqrt[6] x] - 
   E^(6 x) (17/21 - 4 x + 7 x^2) // Simplify

Out[208]= True
POSTED BY: Erik Mahieu
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