The answer is TRUE and FALSE but for the first question I don't even understand what is asked? what is H(x,y)? Why is it True?
2026-04-12 08:42:07.1775983327
Differential equation help with a problem true/false
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Take $y(x) = -x^2$ and notice that it satisfies the equation. I would say that you can take $H(x,y) = y+x^2$. Notice that $H(0,0)=0$ and hence $H(x,y(x)) = H(0,0)$ turns to be $$ y(x) + x^2 = 0, $$ that gives $y(x) = -x^2$, i.e., the solution to the differential equation. This proves that the first claim is true.