Consider the autonomous ODE y’=f(y) and compute the consistency order of the explicit Euler method

Question

Consider the autonomous ODE $y’=f(y)$ and compute the consistency order of the explicit Euler method. I’m not sure whether my solution is correct. Please help me to correct it if there is any problem. Thanks! My solution to this problem is \begin{align} \tau(s,y,h,f)&=\frac{y(s+h)-\psi(s,y,h,f)}{h} \\[.5em] \psi(s,y,h,f)&=y(s)+hf(y(s)) \\[.5em] \tau(s,y,h,f)&=\frac{y(s+h)-y(s)-hf(y(s))}{h} \\&=\frac{y(s)+y{}’(s)h+\frac{1}{2}y{}’’(s)h^2+O(h^3)-y(s)-h{}’(s)}{h} \\&=\frac{\frac{1}{2}y{}’’(s)h^2+O(h^3)}{h} =\frac{1}{2}y{}’’(s)h+O(h^2)=O(h) \end{align}