73.16.18 problem 24.3 (b)

Internal problem ID [15530]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.3 (b)
Date solved : Tuesday, January 28, 2025 at 08:01:22 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 30

dsolve(x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)+6*x*diff(y(x),x)-6*y(x)=x^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 34

DSolve[x^3*D[y[x],{x,3}]-3*x^2*D[y[x],{x,2}]+6*x*D[y[x],x]-6*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^3 \log (x)+x \left (\left (-\frac {3}{4}+c_3\right ) x^2+c_2 x+c_1\right ) \]