Performance issues when drawing multiple plots of the same solution of a system of ODEs

Question

I defined a system of ODEs inside a Manipulate environment. I would like to draw multiple plots of the same NDSolve solution, i.e. I want to plot each variable separately. My code is pretty straightforward (see a little working example below), but I have performance issues.

My guess is that NDSolve is evaluated every time is called inside a Plot. Is there a way to avoid that? Am I doing something wrong (I am an absolute beginner with Mathematica)?

Here is a minimal working example:

Manipulate[
 Module[{sol, t, a, b, kb = 1.0},
  sol = NDSolve[
    {a'[t] == kb*b[t],
     b'[t] == -ka*b[t],
     a[0] == 0.1, b[0] == 0.1},
    {a, b}, {t, 0.0, 5.0}];
  GraphicsRow[{
    Plot[a[t] /. sol, {t, 0.0, 5.0}],
    Plot[b[t] /. sol, {t, 0.0, 5.0}]}
   ]
  ],
 {{ka, 1.0, "ka"}, 1.0, 100.0}
]

Answer 1

One way is to use DSolve and solve the ODE once, then replace the parameter ka into the solution. Now it is very fast

Manipulate[

GraphicsRow[{
   Plot[a[t]/.sol/.{ka0->ka},{t,0.0,5.0}],
   Plot[b[t]/.sol/.{ka0->ka},{t,0.0,5.0}]
}
],
{{ka,1.0,"ka"},1.0,100.0},
TrackedSymbols:>{ka},
Initialization:>
{
  kb=1;
  sol=First@DSolve[{a'[t]==kb*b[t],b'[t]==-ka0*b[t],a[0]==1/10,b[0]==1/10},
     {a[t],b[t]},t]
}    
]

Notice that when using Initialization section in Manipulate, the symbols in there become global.

Update

To answer comment below. If there is no closed form solution, then the same thing can be done but using ParametricNDSolve as follows

Manipulate[

GraphicsRow[{
  Plot[a[ka][t]/.sol ,{t,0.0,5.0}],
  Plot[b[ka][t]/.sol ,{t,0.0,5.0}]
}
],
  {{ka,1.0,"ka"},1.0,100.0},
  TrackedSymbols:>{ka},

Initialization:>
{
  kb=1;
  sol=ParametricNDSolve[{a'[t]==kb*b[t],b'[t]== 
          - ka0*b[t],a[0]==1/10,b[0]==1/10},{a,b},{t,0,5},{ka0}]
}    
]