62.27.5 problem Ex 5

Internal problem ID [12943]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of undetermined coefficients. Page 107
Problem number : Ex 5
Date solved : Tuesday, January 28, 2025 at 04:44:45 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (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]
 

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