a) Construct a linear first-order differential equation of the form xy' + a0(x)y = g(x)
Chapter 2, Problem 45(choose chapter or problem)
a) Construct a linear first-order differential equation of the form xy' + a0(x)y = g(x) for which ye= c!x3 and y P = x3. Give an interval on which y = x3 + c!x3 is the general solution of the DE. (b) Give an initial condition y(x0) = y0 for the DE found in part (a) so that the solution of the IVP is y = x3 - l/x3. Repeat if the solution is y = x3 + 2/x3. Give an interval I of definition of each of these solutions. Graph the solution curves. Is there an initial-value problem whose solution is defined on the interval (-oo, oo)? (c) Is each IVP found in part (b) unique? That is, can there be more than one IVP for which, say, y = x3 - l!x3, x in some interval/, is the solution?
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