73.13.31 problem 20.4 (g)

Internal problem ID [15409]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.4 (g)
Date solved : Tuesday, January 28, 2025 at 07:54:44 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(x^4*diff(y(x),x$4)+2*x^3*diff(y(x),x$3)+x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_{1} +\ln \left (x \right ) c_{2} +c_{3} \ln \left (x \right )^{2}+c_4 \ln \left (x \right )^{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 29

DSolve[x^4*D[y[x],{x,4}]+2*x^3*D[y[x],{x,3}]+x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (c_4 \log ^3(x)+c_3 \log ^2(x)+c_2 \log (x)+c_1\right ) \]