The curve $C$, where $y \ge 0$, is such that it satisfies the following differential equati

Question

The curve $C$, where $y \ge 0$, is such that it satisfies the following differential equation $$(1+x^2)y \frac{\mathrm{d}y}{\mathrm{d}x} + 2xy^2 = 0,$$ where $y = 1$ when $x = 0$. By using the substitution $z = y^2$, solve the differential equation and find the value of $y$ when $x = 1$.[5]

Accepted Answer

$y=\dfrac1{1+x^2}$ When $x=1$, $y=\dfrac12$

2020 NYJC P1 Q7

2020 NYJC P1 Q7

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