Internal problem ID [2158]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 19.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y=x \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)+diff(y(x),x)-2*y(x)=x*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (5 x^{2}+50 c_{3} -8 x \right ) {\mathrm e}^{2 x}}{50}+\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 39
DSolve[y'''[x]-2*y''[x]+y'[x]-2*y[x]==x*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{250} e^{2 x} \left (25 x^2-40 x+22+250 c_3\right )+c_1 \cos (x)+c_2 \sin (x) \]