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Magazine Problem 5
Find general solutions of the linear systems in Problems 1 through 20. If initial conditions are given, find the particular solution that satisfies them. In Problems 1 through 6, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system. $$ x^{\prime}=-3 x-4 y, y^{\prime}=2 x+y $$
Problem 10
Problems 1 through 10, transform the given differential equation or system into an equivalent system of first-order differential equations. $$ x^{\prime \prime}=(1-y) x, y^{\prime \prime}=(1-x) y $$
Problem 13
Find general solutions of the linear systems in Problems 1 through 20. If initial conditions are given, find the particular solution that satisfies them. In Problems 1 through 6, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system. $$ x^{\prime \prime}=-5 x+2 y, y^{\prime \prime}=2 x-8 y $$
Problem 15
Find general solutions of the linear systems in Problems 1 through 20. If initial conditions are given, find the particular solution that satisfies them. In Problems 1 through 6, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system. $$ x^{\prime \prime}-3 y^{\prime}-2 x=0, y^{\prime \prime}+3 x^{\prime}-2 y=0 $$
