15.13.3 problem 3

Internal problem ID [3172]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 22, page 99
Problem number : 3
Date solved : Monday, January 27, 2025 at 07:24:55 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2,y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{3 x}+c_{1} {\mathrm e}^{2 x}+\frac {x^{2}}{6}+\frac {5 x}{18}+\frac {19}{108} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2}{6}+\frac {5 x}{18}+c_1 e^{2 x}+c_2 e^{3 x}+\frac {19}{108} \]