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Magazine Chapter 12: Simple Linear Regression and Correlation
Q56E
In Problems 7鈥�12 match each of the given differential equations with one or more of these solutions:
(a) \(y = 0\), (b) \(y = 2\), (c) \(y = 2x\), (d) \(y = 2{x^2}\)
\(y' = 2\)
Q57E
In Problems 7鈥�12 match each of the given differential equations with one or more of these solutions:
(a) \(y = 0\), (b) \(y = 2\), (c) \(y = 2x\), (d) \(y = 2{x^2}\)
\(y' = 2y - 4\)
Q58E
In Problems 7鈥�12 match each of the given differential equations with one or more of these solutions:
(a) \(y = 0\), (b) \(y = 2\), (c) \(y = 2x\), (d) \(y = 2{x^2}\)
\(xy' = y\)
Q59E
In Problems 7鈥�12 match each of the given differential equations with one or more of these solutions:
(a) \(y = 0\), (b) \(y = 2\), (c) \(y = 2x\), (d) \(y = 2{x^2}\)
\(y'' + 9y = 18\)
Q5E
In Problems \(1 - 8\( state the order of the given ordinary differential equation. Determine whether the equation is linear or nonlinear by matching it with \((6)\(.
\({\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^2} = \sqrt {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} \(
Q60E
In Problems 7鈥�12 match each of the given differential equations with one or more of these solutions:
(a) \(y = 0\), (b) \(y = 2\), (c) \(y = 2x\), (d) \(y = 2{x^2}\)
\(xy'' - y' = 0\)
Q61E
In Problems \(13\) and \(14\) determine by inspection at least one solution of the given differential equation.
\(y'' = y'\)
Q62E
In Problems \(13\) and \(14\) determine by inspection at least one solution of the given differential equation.
\(y' = y(y - 3)\)
Q63E
In Problems \(15\) and \(16\) interpret each statement as a differential equation.
On the graph of \(y = \phi (x)\) the slope of the tangent line at a point \(P(x,y)\) is the square of the distance from \(P(x,y)\) to the origin.
Q64E
In Problems \(15\) and \(16\) interpret each statement as a differential equation.
On the graph of \(y = \phi (x)\) the rate at which the slope changes with respect to x at a point \(P(x,y)\) is the negative of the slope of the tangent line at \(P(x,y)\).
