Internal problem ID [2226]
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: 25.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y=x^{2} {\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=x^2*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-x^{3}+3 c_{2} -6 x \right ) {\mathrm e}^{2 x}}{3}+{\mathrm e}^{x} c_{1} +c_{3} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 37
DSolve[y'''[x]-6*y''[x]+11*y'[x]-6*y[x]==x^2*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (e^x \left (-\frac {x^3}{3}-2 x+c_2\right )+c_3 e^{2 x}+c_1\right ) \]