Internal problem ID [7483]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y=x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} \left (-27 x^{4} {\mathrm e}^{3 x}+36 x^{3} {\mathrm e}^{3 x}+24 \,{\mathrm e}^{3 x} x -36 \,{\mathrm e}^{3 x} x^{2}-8 \,{\mathrm e}^{3 x}+216 x +216\right )}{1944}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-2 x}+c_{3} x \,{\mathrm e}^{x}+c_{4} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.234 (sec). Leaf size: 64
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]
\[ y(x)\to e^x \left (\frac {x^4}{72}-\frac {x^3}{54}+\left (\frac {1}{54}+c_4\right ) x^2+\left (-\frac {1}{81}+c_3\right ) x+\frac {1}{243}+c_2\right )-\frac {1}{9} e^{-2 x} (x+1-9 c_1) \]