56.3.17 problem 17

Internal problem ID [8875]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 17
Date solved : Monday, January 27, 2025 at 05:11:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-4*y(x) = x,y(x), singsol=all)
 

\[ y = c_{2} x^{2}+\frac {c_{1}}{x^{2}}-\frac {x}{3} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 23

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x] == x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^2+\frac {c_1}{x^2}-\frac {x}{3} \]