Wrong Differential Equations solutions?

[rax1994 (Pawel Wozniak)]

Hello everyone.
I tried to verify my solutions of Differential Equations today and I keep getting wrong results, at least I believe so.

there is obviously a solution of c=1

and here it should be “y(t)=c1+cos(2t)/4” instead.
Interesting enough, if you change 2 to 3 you will get a good result.
Of course here it doesn’t calculate a particular solution either (eg. for given y=2 when t=(pi)/2).

[thonan (Terrence Honan)]

y=5 is interpreted as a constant function by Alpha. Try “3dy/dx+x=6 where y(3)=5.5”.

[rax1994 (Pawel Wozniak)]

Right, it works. Thank you sir.
What about the second one?

[thonan (Terrence Honan)]

That is equivalent by trig identities. The constant c_1 is different, though.

[rax1994 (Pawel Wozniak)]

Correct. I feel stupid asking after all, should’ve checked that. Doing maths at 3:30 in the morning isn’t the best idea for me apparently.
Thanks again.