(20) Classify the following as an ordinary differential equation or a partial differential equation, give the order, and indicate the independent and dependent variables. If the equation is an ODE,

indicate whether the equation is linear or non linear. \frac{d y}{d x}=k y(c-y), \text { where } k \text { and } c \text { are constants } \frac{d x}{d t}=k(4-t)^{4}(2-t), \text { where } k \text { is a constant } \frac{\partial u}{\partial t}=\frac{\partial^{2} u}{\partial r^{2}}+\frac{1}{u} \frac{\partial u}{\partial r}+k u, \text { where } k \text { is a constant } \frac{d^{2} y}{d x^{2}}+2 \frac{d y d^{3} y}{d x} \frac{d x^{3}}+x^{2}=0