10.16 problem 16

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]]

Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+y a^{2}-x^{1+a}=0} \end {gather*}

Solution by Maple

Time used: 0.009 (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)
 

\[ y \relax (x ) = x^{a} c_{2}+x^{a} \ln \relax (x ) c_{1}+x^{a +1} \]

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*}