Euler Equations. An equation of the formt2 d2ydt2 + tdydt
Chapter 3, Problem 34(choose chapter or problem)
Euler Equations. An equation of the formt2 d2ydt2 + tdydt + y = 0, t > 0, (ii)where and are real constants, is called an Euler equation.(a) Let x = ln t and calculate dy/dt and d2y/dt2 in terms of dy/dx and d2y/dx2.(b) Use the results of part (a) to transform Eq. (ii) intod2ydx2 + ( 1)dydx + y = 0. (iii)Observe that Eq. (iii) has constant coefficients. If y1(x) and y2(x) form a fundamental setof solutions of Eq. (iii), then y1(ln t) and y2(ln t) form a fundamental set of solutions ofEq. (ii).
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