64.13.19 problem 19

Internal problem ID [13549]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 05:52:38 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 23

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

\[ y = \frac {x \left (4 \ln \left (x \right ) c_{3} +4 c_{2} x +x^{2}+4 c_{1} \right )}{4} \]

✓ Solution by Mathematica

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

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

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