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2.5 Euler’s Differential Equation 75
2
14. x y + 25xy + 144y = 0; y(1) =−4, y (1) = 0 equation to obtain a quadratic equation for r. Roots of
r
this quadratic equation yield solutions y = x . Use this
2
15. x y − 9xy + 24y = 0; y(1) = 1, y (1) = 10
approach to solve the Euler equations of Examples
2
16. x y + xy − 4y = 0; y(1) = 7, y (1) =−3 2.22, 2.22, and 2.23.
17. Here is another approach to solving an Euler equa- 18. Outline a procedure for solving the Euler equation for
tion. For x > 0, substitute y = x into the differential x < 0. Hint:Let t = ln|x| in this case.
r
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