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: 0.0 (sec). Leaf size: 41
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)
\[ y \left (x \right ) = \frac {\left (\left (x^{2}+\frac {5}{2} x +\frac {23}{8}\right ) {\mathrm e}^{4 x}+8 \,{\mathrm e}^{6 x} c_{2} +8 c_{3} {\mathrm e}^{5 x}-\frac {8 c_{1}}{5}\right ) {\mathrm e}^{-5 x}}{8} \]
✓ 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]
\[ y(x)\to \frac {1}{64} e^{-x} \left (8 x^2+20 x+23\right )-\frac {1}{5} c_1 e^{-5 x}+c_2 e^x+c_3 \]