Internal problem ID [11797]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 23.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }=18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 64
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)-3*diff(y(x),x$2)=18*x^2+16*x*exp(x)+4*exp(3*x)-9,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\left (x^{4}+\frac {8}{3} x^{3}+\frac {19}{3} x^{2}-2 c_{3} x -2 c_{4} \right ) {\mathrm e}^{3 x}+\left (-4 x^{2}+18 x -2 c_{2} -\frac {57}{2}\right ) {\mathrm e}^{4 x}-\frac {2 c_{1}}{9}-\frac {2 \,{\mathrm e}^{6 x}}{27}\right ) {\mathrm e}^{-3 x}}{2} \]
✓ Solution by Mathematica
Time used: 1.232 (sec). Leaf size: 70
DSolve[y''''[x]+2*y'''[x]-3*y''[x]==18*x^2+16*x*Exp[x]+4*Exp[3*x]-9,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{6} \left (3 x^2+8 x+19\right ) x^2+\frac {1}{4} e^x \left (8 x^2-36 x+57+4 c_2\right )+\frac {e^{3 x}}{27}+c_4 x+\frac {1}{9} c_1 e^{-3 x}+c_3 \]