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The function can be seen on the picture. I should show that y(0)=0 but I stuck at the step you see on the picture. It seems possible at that step that y(0)=0 is a solution but there still might be others too.

without knowing what y(x) looks like, the best we can say is the equation is true for y(0)=0

Thank you ZeHanz for your help.

yw!