44.3.21 problem 29

Internal problem ID [7002]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 29
Date solved : Monday, January 27, 2025 at 02:40:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(x^2*diff(y(x),x$2)+(x^2-x)*diff(y(x),x)+(1-x)*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_{2} \operatorname {Ei}_{1}\left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 17

DSolve[x^2*D[y[x],{x,2}]+(x^2-x)*D[y[x],x]+(1-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (c_2 \operatorname {ExpIntegralEi}(-x)+c_1) \]