(Solved): Consider the differential equation. \[ x \frac{d y}{d x}-4 \sqrt{y^{2}-64 x^{ ...

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Consider the differential equation. \[ x \frac{d y}{d x}-4 \sqrt{y^{2}-64 x^{2}}=y, y>0 \] Chapter 2, Section 2.7, Question 08 (a) Determine if the equation is homogeneous. The differential equation homogeneous. eTextbook and Media Hint Using multiple attempts will impact your score. \( 10 \% \) score reduction after attempt 2 Chapter 2, Section 2.7, Question 08 (b) If it is homogeneous, then solve the differential equation. Select the correct answer. The general solution is \[ \begin{array}{l} \ln \left[\frac{y}{x}+\sqrt{\frac{y^{2}}{x^{2}}-64 x} \mid=\ln \left(x^{4}\right)+c\right. \\ \ln \left[\frac{y}{x}-\sqrt{\frac{y^{2}}{x^{2}}-64}\right]=\ln \left(x^{4}\right)+c \\ \ln \left[\frac{y}{x}+\sqrt{\frac{y^{2}}{x^{2}}-64}\right]=\ln \left(x^{4}\right)+c \\ \ln \left[\frac{y}{x}+\sqrt{\frac{y^{2}}{x^{2}}+64}\right]=\ln \left(x^{4}\right)+c \end{array} \]