An equation of the form 12dy dt where a and are real constants, is called an...

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An equation of the form 12dy dt where a and are real constants, is called an Euler equation. If we let x = In t and calculate dy/dt and dy/dt in terms of dy/dx and dy/dx, then equation (1) becomes dy + (x - 1)dy + By = dx dx + at dy+ By = 0, t> 0, (1) dt = 0. (2) Observe that equation (2) has constant coefficients. If y(x) and y(x) form a fundamental set of solutions of equation (2), then y(In t) and y2(In t) form a fundamental set of solutions of equation (1). Use the substitution above to solve the given differential equation. 2ty" - 9ty' +9y = 0, t> 0 y(t): ce(4+ (4+7)ln(1) + cze(47)In(t) X An equation of the form 12dy dt where a and are real constants, is called an Euler equation. If we let x = In t and calculate dy/dt and dy/dt in terms of dy/dx and dy/dx, then equation (1) becomes dy + (x - 1)dy + By = dx dx + at dy+ By = 0, t> 0, (1) dt = 0. (2) Observe that equation (2) has constant coefficients. If y(x) and y(x) form a fundamental set of solutions of equation (2), then y(In t) and y2(In t) form a fundamental set of solutions of equation (1). Use the substitution above to solve the given differential equation. 2ty" - 9ty' +9y = 0, t> 0 y(t): ce(4+ (4+7)ln(1) + cze(47)In(t) X