Internal problem ID [1170]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+y a^{2}-x^{1+a}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)-(2*a-1)*x*diff(y(x),x)+a^2*y(x)=x^(a+1),y(x), singsol=all)
\[ y \left (x \right ) = x^{a} c_{2} +x^{a} \ln \left (x \right ) c_{1} +x^{a +1} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 19
DSolve[x^2*y''[x]-(2*a-1)*x*y'[x]+a^2*y[x]==x^(a+1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^a (a c_2 \log (x)+x+c_1) \\ \end{align*}