53 Solve homogeneous 1st order linear differential equation with constant coefficients and initial conditions

Problem: Solve

$$y^{\prime}\left( t\right) =3y\left( t\right)$$

with initial condition $y\left( 0\right) =1$ and plot the solution for $t=0 \cdots 2$ seconds.

Mathematica	Matlab
Remove["Global`*"]; sol = First@DSolve[{y'[t]==3y[t],y[0]==1},y[t],t]; y = y[t]/.sol Out[26]= E^(3 t) Plot[y,{t,0,2}, FrameLabel->{{"y(t)",None}, {"t","Solution of y'=3y, y(0)=1"}}, Frame->True, GridLines->Automatic, GridLinesStyle->Automatic, RotateLabel->False, ImageSize->300, AspectRatio->1]	function e53 t = 0:0.001:2; % time initial_y = 1; [t,y] = ode45( @rhs, t, initial_y); plot(t,y) title('Solution of y''=3y , y(0)=1, using ode45'); xlabel('time'); ylabel('y(t)'); grid on set(gcf,'Position',[10,10,420,420]); function dydt=rhs(t,y) dydt = 3*y; end end