44.1.37 problem 39

Internal problem ID [6912]
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. Exercises 1.1 at page 12
Problem number : 39
Date solved : Monday, January 27, 2025 at 02:34:48 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+15*y(x)=0,y(x), singsol=all)
 

\[ y = x^{3} \left (c_{1} x^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.125 (sec). Leaf size: 133

DSolve[x^2*D[y[x],{x,2}]-7*D[y[x],x]+15*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 7^{-\frac {1}{2} i \left (\sqrt {59}-i\right )} x^{\frac {1}{2}-\frac {i \sqrt {59}}{2}} \left (c_2 x^{i \sqrt {59}} \operatorname {Hypergeometric1F1}\left (-\frac {1}{2}-\frac {i \sqrt {59}}{2},1-i \sqrt {59},-\frac {7}{x}\right )+7^{i \sqrt {59}} c_1 \operatorname {Hypergeometric1F1}\left (\frac {1}{2} i \left (i+\sqrt {59}\right ),1+i \sqrt {59},-\frac {7}{x}\right )\right ) \]