Internal problem ID [2200]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 22, page 99
Problem number: 2.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (\frac {1}{6} x^{3}+c_{1} +c_{2} x +c_{3} x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 32
DSolve[y'''[x]-3*y''[x]+3*y'[x]-y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^x \left (x^3+6 c_3 x^2+6 c_2 x+6 c_1\right ) \]