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Magazine Problem 8
In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. Circles with center on the \(x\) -axis.
Problem 8
For each of the following, state whether the equation is ordinary or partial, linear or nonlinear, and give its order. \(\frac{d^{4} y}{d x^{4}}=w(x)\)
Problem 9
In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. Circles with fixed radius \(r\) and tangent to the \(x\) -axis.
Problem 9
For each of the following, state whether the equation is ordinary or partial, linear or nonlinear, and give its order. \(x \frac{d^{2} y}{d t^{2}}-y \frac{d^{2} x}{d t^{2}}=c_{1}\)
Problem 10
For each of the following, state whether the equation is ordinary or partial, linear or nonlinear, and give its order. \(L \frac{d i}{d t}+R i=E\)
Problem 10
In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. Circles tangent to the \(x\) -axis.
Problem 11
In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. Circles with center on the line \(y=-x\), and passing through the origin.
Problem 11
In each of the following eliminate the arbitrary constants. $$ y=c_{1}+c_{2} e^{3 x} $$
Problem 11
For each of the following, state whether the equation is ordinary or partial, linear or nonlinear, and give its order. \((x+y) d x+\left(3 x^{2}-1\right) d y=0\)
Problem 12
For each of the following, state whether the equation is ordinary or partial, linear or nonlinear, and give its order. \(x\left(y^{\prime \prime}\right)^{3}+\left(y^{\prime}\right)^{4}-y=0\)
