An equation of the form t2 d2y dt2 + αt dy dt + βy = 0, t > 0, (1) where α and β are real constants, is called an Euler equation. If we let x = ln t and calculate dy/dt and d2y/dt2 in terms of dy/dx and d2y/dx2, then equation (1) becomes d2y dx2 + (α − 1) dy dx + βy = 0. (2) Observe that equation (2) has constant coefficients. If y1(x) and y2(x) form a fundamental set of solutions of equation (2), then y1(ln t) and y2(ln t) form a fundamental set of solutions of equation (1). Use the method above to solve the given equation for t > 0. t2y'' + 5ty' + 3y = 0