Internal problem ID [2221]
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: 20.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }=x^{2} {\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(x),x$3)+4*diff(y(x),x$2)-5*diff(y(x),x)=x^2*exp(-x),y(x), singsol=all)
\[ y = \frac {23 \,{\mathrm e}^{-x}}{64}+c_{1} {\mathrm e}^{x}-\frac {{\mathrm e}^{-5 x} c_{2}}{5}+\frac {5 \,{\mathrm e}^{-x} x}{16}+\frac {x^{2} {\mathrm e}^{-x}}{8}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.192 (sec). Leaf size: 44
DSolve[y'''[x]+4*y''[x]-5*y'[x]==x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{64} e^{-x} \left (8 x^2+20 x+23\right )-\frac {1}{5} c_1 e^{-5 x}+c_2 e^x+c_3 \]