Internal problem ID [2155]
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: 16.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y=x +{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 77
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+4*diff(y(x),x)-12*y(x)=x+exp(2*x),y(x), singsol=all)
\[ y = \frac {{\mathrm e}^{3 x} {\mathrm e}^{-3 x} \cos \left (2 x \right )}{52}+\frac {3 \,{\mathrm e}^{3 x} {\mathrm e}^{-3 x} \sin \left (2 x \right )}{104}-\frac {{\mathrm e}^{-3 x} \left (6 \,{\mathrm e}^{3 x} x +9 \,{\mathrm e}^{5 x}+2 \,{\mathrm e}^{3 x}\right )}{72}+\cos \left (2 x \right ) c_{1} +{\mathrm e}^{3 x} c_{2} +c_{3} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.337 (sec). Leaf size: 45
DSolve[y'''[x]-3*y''[x]+4*y'[x]-12*y[x]==x+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{72} \left (-6 x-9 e^{2 x}+72 c_3 e^{3 x}-2\right )+c_1 \cos (2 x)+c_2 \sin (2 x) \]