(Solved): Interpret the statement as a differential equation. (Use \( y p \) for \( y^{\prime} \) and \( y p ...

Interpret the statement as a differential equation. (Use \( y p \) for \( y^{\prime} \) and \( y p p \) for \( y^{\prime \prime} \).) On the graph of \( y=\varphi(x) \), the slope of the tangent line at a point \( P(x, y) \) is the square of the distance from \( P(x, y) \) to the origin. \[ y_{p}=x^{2}+y^{2} \]