15.11.9 problem 9

Internal problem ID [3119]
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 : 9
Date solved : Monday, January 27, 2025 at 07:21:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y&=x +{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.184 (sec). Leaf size: 36

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

\[ y(x)\to -\frac {x}{4}+e^{2 x} \left (\frac {x}{4}-\frac {1}{16}+c_1\right )+c_2 e^{-2 x} \]