Internal problem ID [13474]
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).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y=x^{3}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y = -\frac {3 x^{3}}{4}+\frac {\ln \left (x \right ) x^{3}}{2}+c_{3} x^{3}+c_{2} x^{2}+c_{1} x \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 34
DSolve[x^3*y'''[x]-3*x^2*y''[x]+6*x*y'[x]-6*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x^3 \log (x)+x \left (\left (-\frac {3}{4}+c_3\right ) x^2+c_2 x+c_1\right ) \]