please help me (dsolve)

im sure its correct but it doesnt work

w=dsolve('D2y+0.5*Dy+y=3','y(0)=0.5,Dy(0)=0');

matlab 2018

im grateful for your help

Answer 1

[Star Strider]

The single quotation marks are likely the problem.

Try this slightly edited version:

syms y(t) 
Dy = diff(y);
D2y = diff(Dy);
w = dsolve( D2y+0.5*Dy+y == 3, y(0) == 0.5, Dy(0) == 0 );
w = simplify(w, 'Steps',250)

figure
fplot(w, [0 30])
grid
xlabel('t')
ylabel('w(t)')
ltxw = latex(w);
title(['$w(t) = ' ltxw '$'], 'Interpreter','latex')

producing:

.

[Melika Eft]

Thank you

Answer 2

[Mischa Kim]

Use instead

syms y(t)
eqn  = diff(y,t,2) + 0.5*diff(y,t) + y == 3;
Dy   = diff(y,t);
cond = [y(0) == 0.5, Dy(0) == 0];
w    = dsolve(eqn,cond)

[Melika Eft]

Thank you