Internal problem ID [1129]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page
253
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x^{a} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([x^2*diff(y(x),x$2)-(2*a-1)*x*diff(y(x),x)+a^2*y(x)=0,x^a],singsol=all)
\[ y \left (x \right ) = \left (c_{2} \ln \left (x \right )+c_{1} \right ) x^{a} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 18
DSolve[x^2*y''[x]-(2*a-1)*x*y'[x]+a^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^a (a c_2 \log (x)+c_1) \]