Internal problem ID [6727]
Book: Second order enumerated odes
Section: section 2
Problem number: 42.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y-x \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 78
dsolve(diff(y(x),x$4)-diff(y(x),x$3)-3*diff(y(x),x$2)+5*diff(y(x),x)-2*y(x)=x*exp(x)+3*exp(-2*x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{-2 x} \left (-27 x^{4} {\mathrm e}^{3 x}+36 x^{3} {\mathrm e}^{3 x}+24 \,{\mathrm e}^{3 x} x -36 \,{\mathrm e}^{3 x} x^{2}-8 \,{\mathrm e}^{3 x}+216 x +216\right )}{1944}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-2 x}+c_{3} x \,{\mathrm e}^{x}+c_{4} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.314 (sec). Leaf size: 59
DSolve[y''''[x]-y'''[x]-3*y''[x]+5*y'[x]-2*y[x]==x*Exp[x]+3*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (\frac {1}{648} x (3 x (x (3 x-4)+4+216 c_4)-8+648 c_3)+\frac {1}{243}+c_2\right )-\frac {1}{9} e^{-2 x} (x+1-9 c_1) \\ \end{align*}