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Magazine Problem 1
Form the differential equation in each of the following cases by eliminating the parameters mentioned against each. $$ y=a x+b x^{2} $$
Problem 2
Form the differential equation in each of the following cases by eliminating the parameters mentioned against each. $$ x=A \cos (p t+B) \quad(A, B) $$
Problem 3
Form the differential equation in each of the following cases by eliminating the parameters mentioned against each. $$ y=m x+\frac{a}{m} $$
Problem 4
Form the differential equation in each of the following cases by eliminating the parameters mentioned against each. $$ y=a x^{2}+b x+c \quad(a, b, c) $$
Problem 5
Form the differential equation in each of the following cases by eliminating the parameters mentioned against each. $$ (x-h)^{2}+(y-k)^{2}=r^{2} $$
Problem 6
Form the differential equation in each of the following cases by eliminating the parameters mentioned against each. $$ y=e^{x}(A \cos x+B \sin x) \quad(A, B) $$
Problem 7
Find the differential equation for the family of circles with their centres on the \(x\) -axis. (Hint: \(x^{2}+y^{2}+2 g x+c=0 g, c\) parameters \()\)
Problem 8
Form the differential equation for the family of circles, touching the \(x\) -axis at \((0,0)\). (Hint: \(x^{2}+y^{2}-2 f y=0, f\) parameter)
Problem 9
Form the differential equation of all parabolas each having its latus-return \(=4 a\) and its axis parallel to the \(x\) -axis. (Hint: \((y-k)^{2}=4 a(x-h) ; h, k\) parameters)
Problem 10
Find the differential equation by eliminating \(c\) from \(y=c x+x^{3}\).
