Given the differential equation

y′=2ty2+7,y(0)=0\displaystyle {y}'={2}{t}{y}^{{2}}+{7},\quad{y}{\left({0}\right)}={0}

Find the corresponding Picard iterates y1(t)\displaystyle {y}_{{1}}{\left({t}\right)} and y2(t)\displaystyle {y}_{{2}}{\left({t}\right)}. Then find the uniform norm of their difference, ∣∣y2−y1∣∣\displaystyle {\left|{\left|{y}_{{2}}-{y}_{{1}}\right|}\right|} on the interval [0,1].

y1(t)\displaystyle {y}_{{1}}{\left({t}\right)} =  

y2(t)\displaystyle {y}_{{2}}{\left({t}\right)} =  

∣∣y2−y1∣∣\displaystyle {\left|{\left|{y}_{{2}}-{y}_{{1}}\right|}\right|} =  

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