7.11.24 problem 24

Internal problem ID [345]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 24
Date solved : Monday, January 27, 2025 at 02:46:07 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-12 y^{\prime }&=x -2 x \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 45

dsolve(diff(y(x),x$3)-diff(y(x),x$2)-12*diff(y(x),x)=x-2*x*exp(-3*x),y(x), singsol=all)
 

\[ y = -\frac {\left (\left (x^{2}-\frac {1}{6} x -24 c_3 \right ) {\mathrm e}^{3 x}+\frac {8 x^{2}}{7}-6 \,{\mathrm e}^{7 x} c_1 +\frac {160 x}{147}+8 c_2 +\frac {1264}{3087}\right ) {\mathrm e}^{-3 x}}{24} \]

✓ Solution by Mathematica

Time used: 0.316 (sec). Leaf size: 54

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]-12*D[y[x],x]==x-2*x*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^2}{24}-\frac {e^{-3 x} \left (441 x^2+420 x+158+3087 c_1\right )}{9261}+\frac {x}{144}+\frac {1}{4} c_2 e^{4 x}+c_3 \]