sol=DSolve[{v'[t] == 9.8 - 0.2 v[t],  
          v[0] == c},  v[t], t]

v[t_] = v[t] /. First[sol]

Clear [y, x]

    sol1 = 
      DSolve[y''[x] + 2  y'[x] + y[x] == 4 E^(-x),  
        y[x], x]

Clear[y, x]
DSolve[{y''[x] - y'[x] - 2  y[x] == 0,  
        y[0] == a,  y'[0] == b},  y[x], x]

sol2 = 
      DSolve[{y''[x] - 2  y'[x] + 5 y[x] == 0,  
          y[π/2] == 0,  y'[π/2] == 2}, y[x], 
        x]

y[x_] = y[x] /. First[sol2]

Plot[y[x],  {x,  2,  10}]

Clear[y, x]; 
    sol3 = DSolve[{y''[x] + 2 y'[x] + 5 y[x] == 
              4 E^(-x) Cos[2  x], 
            y[0] == 1,  y'[0] == 0}, y[x], x] // 
        Simplify

z[x_] = y[x] /. First[sol3]

Plot[z[x], {x, 0, 10},  PlotStyle -> {Red}, 
      PlotRange -> All,  AspectRatio -> 0.7]