15.12.13 problem 13

Internal problem ID [3157]
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 : 13
Date solved : Monday, January 27, 2025 at 07:24:08 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 30

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

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