15.14.19 problem 19

Internal problem ID [3191]
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 : 19
Date solved : Monday, January 27, 2025 at 07:25:49 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 40

dsolve(diff(y(x),x$3)-y(x)=x^2,y(x), singsol=all)
 

\[ y = -x^{2}+{\mathrm e}^{x} c_{1} +c_2 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 59

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

\[ y(x)\to -x^2+c_1 e^x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_3 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \]