Question

hi just want to ask how do I find the general solution of x'+x=0 ; x(0)=1 , x'(0)=0

Answer 1

mutiply both sides by e^x, this allows you to undo the product rule in this case

Answer 2

\[(fg)'=f'g+fg'\]
seeing how youve got f'+f, it only makes sense to multiply it thru by a function that is its own derivative

Answer 3

\[x'+x=0\]
\[x'e^x+xe^x=0\]
\[xe^x=C\]
something like that

Answer 4

maybe e^t to represent this as a function of t .... just to pretty it up is all

Answer 5

whoa wait so what does the C go to?