An equation of 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. 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 substitution above to solve the given differential equation. t2y'' − 5ty' + 9y = 0, t > 0