12.10.16 problem 16

Internal problem ID [1820]
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
Date solved : Monday, January 27, 2025 at 05:36:06 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=x^{a +1} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

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)
 

\[ y = x^{a} \left (c_2 +\ln \left (x \right ) c_1 +x \right ) \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 19

DSolve[x^2*D[y[x],{x,2}]-(2*a-1)*x*D[y[x],x]+a^2*y[x]==x^(a+1),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^a (a c_2 \log (x)+x+c_1) \]