15.14.23 problem 23

Internal problem ID [3195]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 23
Date solved : Monday, January 27, 2025 at 07:25:51 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&={\mathrm e}^{2 x} \left (x -3\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)=exp(2*x)*(x-3),y(x), singsol=all)
 

\[ y = \frac {\left (-2 x +7\right ) {\mathrm e}^{2 x}}{16}+c_2 x +\frac {{\mathrm e}^{4 x} c_{1}}{16}+c_3 \]

✓ Solution by Mathematica

Time used: 0.233 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{16} e^{2 x} \left (-2 x+c_1 e^{2 x}+7\right )+c_3 x+c_2 \]