15.11.19 problem 19

Internal problem ID [3129]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 19
Date solved : Monday, January 27, 2025 at 07:22:33 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 31

dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)+diff(y(x),x)-2*y(x)=x*exp(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (5 x^{2}+50 c_3 -8 x \right ) {\mathrm e}^{2 x}}{50}+\cos \left (x \right ) c_{1} +c_2 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 39

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

\[ y(x)\to \frac {1}{250} e^{2 x} \left (25 x^2-40 x+22+250 c_3\right )+c_1 \cos (x)+c_2 \sin (x) \]