ODE and Placing slopes

Questions
,
1

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)))

2

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]))}}
3

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