Identify the dependent and independent variables of the following differential equations. Give the order of the equations and state which are linear. (a) \(\frac{\mathrm{d} y}{\mathrm{~d} x}+9 y=0\) (b) \(\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)\left(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\right)+3 \frac{\mathrm{d} y}{\mathrm{~d} x}=0\) (c) \(\frac{\mathrm{d}^{3} x}{\mathrm{~d} t^{3}}+5 \frac{\mathrm{d} x}{\mathrm{~d} t}=\sin x\)

Question: Identify the dependent and independent variables, the order of the equation, and whether the equation is linear or not for the following differential equations: (a) \( \frac{\mathrm{d} y}{\mathrm{~d} x}+9 y=0\), (b) \(\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)\left(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\right)+3 \frac{\mathrm{d} y}{\mathrm{~d} x}=0\), and (c) \(\frac{\mathrm{d}^{3} x}{\mathrm{~d} t^{3}}+5 \frac{\mathrm{d} x}{\mathrm{~d} t}=\sin x\). Answer: (a) Dependent variable: \(y\), Independent variable: \(x\), Order: 1, Linearity: Linear (b) Dependent variable: \(y\), Independent variable: \(x\), Order: 2, Linearity: Nonlinear (c) Dependent variable: \(x\), Independent variable: \(t\), Order: 3, Linearity: Linear