82.52.4 problem Ex. 4

Internal problem ID [19012]
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 page 116
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:45:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

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

\[ y \left (x \right ) = {\mathrm e}^{x} x \left (c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 17

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

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