82.54.11 problem Ex. 11

Internal problem ID [19027]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at end of chapter at page 120
Problem number : Ex. 11
Date solved : Tuesday, January 28, 2025 at 08:29:26 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 31

dsolve(x^2*diff(y(x),x$3)+x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_3 \left (x +1\right ) {\mathrm e}^{-x}}{2}+x \left (-\frac {c_3 \left (x +2\right ) \operatorname {Ei}_{1}\left (x \right )}{2}+c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 50

DSolve[x^2*D[y[x],{x,3}]+x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (-c_3 x (x+2) \operatorname {ExpIntegralEi}(-x)+x ((c_1+2 c_2) x+4 c_2)-c_3 e^{-x} (x+1)\right ) \]