15.12.10 problem 10

Internal problem ID [3154]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:24:00 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(diff(y(x),x$3)+4*diff(y(x),x$2)-5*diff(y(x),x)=exp(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (5 \,{\mathrm e}^{8 x}+240 c_{1} {\mathrm e}^{6 x}+240 c_3 \,{\mathrm e}^{5 x}-48 c_2 \right ) {\mathrm e}^{-5 x}}{240} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 34

DSolve[D[y[x],{x,3}]+4*D[y[x],{x,2}]-5*D[y[x],x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{3 x}}{48}-\frac {1}{5} c_1 e^{-5 x}+c_2 e^x+c_3 \]