Internal problem ID [13435]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.12 (e).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=x^2,y(x), singsol=all)
\[ y = -x^{2}-2 x +c_{1} \cos \left (x \right )+c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 30
DSolve[y'''[x]-y''[x]+y'[x]-y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x^2-2 x+c_3 e^x+c_1 \cos (x)+c_2 \sin (x) \]