Internal problem ID [2163]
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: 24.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }=\left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 58
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)=(2*x^2+x)*exp(-2*x)+5*cos(3*x),y(x), singsol=all)
\[ y = {\mathrm e}^{-2 x} x +\frac {11 \,{\mathrm e}^{-2 x}}{16}+\frac {5 \,{\mathrm e}^{-2 x} x^{2}}{8}+\frac {{\mathrm e}^{-2 x} x^{3}}{6}+\frac {c_{1} {\mathrm e}^{-2 x}}{4}-\frac {5 \sin \left (3 x \right )}{39}-\frac {10 \cos \left (3 x \right )}{117}+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.974 (sec). Leaf size: 56
DSolve[y'''[x]+2*y''[x]==(2*x^2+x)*Exp[-2*x]+5*Cos[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{48} e^{-2 x} \left (8 x^3+30 x^2+48 x+33+12 c_1\right )-\frac {5}{39} \sin (3 x)-\frac {10}{117} \cos (3 x)+c_3 x+c_2 \]