Chapter 8: Ordinary Differential Equations

Question: In Problems 25to 28, find a particular solution satisfying the given conditions.

when x = 0.

Question: In Problems 25to 28, find a particular solution satisfying the given conditions.

when x = 1

Question: If 10kgof rock salt is placed in water, it dissolves at a rate proportional to the amount of salt still undissolved. If 2kgdissolve during the first 10minutes, how long will it be until only 2kgremain undissolved?

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

Question: A mass mfalls under gravity (force mg) through a liquid whose viscosity is decreasing so that the retarding force is -2mv / ( 1+T ), where v is the speed of m. If the mass starts from rest, find its speed, its acceleration, and how far it has fallen (in terms of g) when t = 1.

Question: The acceleration of an electron in the electric field of a positively charged sphere is inversely proportional to the square of the distance between the electron and the center of the sphere. Let an electron fall from rest at infinity to the sphere. What is the electron’s velocity when it reaches the surface of the sphere?

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

Question: Identify each of the differential equations in Problemsto as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

Question: Identify each of the differential equations in Problemsto as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.