α=-1.5;
eqn1=y'[t]==α*y[t];
eqn2=y[0]==1;

sol=DSolve[{eqn1,eqn2},y[t],t]

Plot[y[t]/.sol,{t,0,10},PlotRange->{{0,10},{0,1}}]

ω=1;
eqn1=y''[t]==ω^2*y[t];
eqn2=y[0]==1;
eqn3=y'[0]==0;

sol2=DSolve[{eqn1,eqn2,eqn3},y[t],t]

Plot[y[t]/.sol2,{t,0,10},PlotRange->{{0,10},{0,100}}]