Example 4.3.1

Integrate[-Sin[t]Tan[t],t]

DSolve[y'''[t]+y'[t]==Tan[t],y[t],t]

DSolve[y'''[t]-y'[t]==Tan[t],y[t],t]

Example 4.3.3

Solve[r^3-2r^2-r+2==0,r]

DSolve[y'''[t]-2y''[t]-y'[t]+2y[t]==Exp[4t],y[t],t]