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ODE and Placing slopes

Posted 9 years ago
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Hello Well, it sounds like I am a Mathematica beginner So I would like some help Can anyone tell me how to solve ode of 1st order and second one. I would like to know the code for these y''+10y'+4y=e^xsinx y''+8y'+4y=3xcosxsinx and how do i plot the slopes for these? Thank you)))

POSTED BY: Altin Guberi
2 Replies

Thank you))) Now can you please also make the phase portrait of it?

POSTED BY: Altin Guberi

The two equal signs imply that you have 3 separate 2nd order DEs. It is unlikely that a solution satisfying all 3 does exists. Assuming just the first and third quantities you can get

In[11]:= DSolve[y''[x] + 10 y'[x] + 4 y[x] == 3 x Cos[x]  Sin[x] , 
 y[x], x]

Out[11]= {{y[x] -> 
   E^((-5 - Sqrt[21]) x) C[1] + E^((-5 + Sqrt[21]) x) C[2] - (
    3 (-2 Cos[2 x] + 10 x Cos[2 x] - 5 Sin[2 x]))/(
    50 (-5 + Sqrt[21])^2 (23 + 5 Sqrt[21]))}}
POSTED BY: S M Blinder
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