Internal problem ID [2210]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 9.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
dsolve(diff(y(x),x$3)-y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+\frac {{\mathrm e}^{x} \left (x +3 c_{1} \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.408 (sec). Leaf size: 62
DSolve[y'''[x]-y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-x/2} \left (e^{3 x/2} (x-1+3 c_1)+3 c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+3 c_3 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]