Internal problem ID [11792]
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: 18.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }=3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)+2*diff(y(x),x$2)=3*exp(-x)+6*exp(2*x)-6*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (6 x +c_{1} -12\right ) {\mathrm e}^{2 x}}{4}-\frac {x^{3}}{2}-\frac {9 x^{2}}{4}+c_{3} x +c_{2} {\mathrm e}^{x}+c_{4} +\frac {{\mathrm e}^{-x}}{2} \]
✓ Solution by Mathematica
Time used: 0.372 (sec). Leaf size: 54
DSolve[y''''[x]-3*y'''[x]+2*y''[x]==3*Exp[-x]+6*Exp[2*x]-6*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-\left ((2 x+9) x^2\right )+2 e^{-x}+4 c_1 e^x+e^{2 x} (6 x-12+c_2)\right )+c_4 x+c_3 \]