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Chapter 12: Q59E (page 535)
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) \(y = 2{x^2}\)
\(y'' + 9y = 18\)
The solution is \({\rm{y = 2}}\).
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(a) Give the domain of the function \(y = {x^{{\textstyle{2 \over 3}}}}\).
(b) Give the largest interval I of definition over which \(y = {x^{{\textstyle{2 \over 3}}}}\) is a solution of the differential equation \(3xy' - 2y = 0\).
(a) Give the domain of the function \(y = {x^{{\textstyle{2 \over 3}}}}\).
(b) Give the largest interval I of definition over which \(y = {x^{{\textstyle{2 \over 3}}}}\) is a solution of the differential equation \(3xy' - 2y = 0\).
In Problems \(13\) and \(14\) determine by inspection at least one solution of the given differential equation.
\(y' = y(y - 3)\)
In Problems \(35\) and \(36\) find values of m so that the function \(y = {m^x}\) is a solution of the given differential equation.
\(xy'' + 2y' = 0\)
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}} \(
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