64.11.18 problem 18

Internal problem ID [13468]
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
Date solved : Tuesday, January 28, 2025 at 05:44:40 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} 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 \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y = \frac {\left (6 x +c_{1} -12\right ) {\mathrm e}^{2 x}}{4}-\frac {x^{3}}{2}-\frac {9 x^{2}}{4}+c_{3} x +{\mathrm e}^{x} c_{2} +c_4 +\frac {{\mathrm e}^{-x}}{2} \]

✓ Solution by Mathematica

Time used: 37.479 (sec). Leaf size: 108

DSolve[D[y[x],{x,4}]-3*D[y[x],{x,3}]+2*D[y[x],{x,2}]==3*Exp[-x]+6*Exp[2*x]-6*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\int _1^{K[4]}e^{K[3]} \left (c_1+e^{K[3]} c_2+\int _1^{K[3]}e^{-2 K[1]} \left (6 e^{K[1]} K[1]-6 e^{3 K[1]}-3\right )dK[1]+e^{K[3]} \int _1^{K[3]}\left (-6 e^{-2 K[2]} K[2]+3 e^{-3 K[2]}+6\right )dK[2]\right )dK[3]dK[4]+c_4 x+c_3 \]