62.25.2 problem Ex 2

Internal problem ID [12934]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 48. Page 103
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:44:20 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 30

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

\[ y = \frac {x^{2}}{3}+\frac {2 x}{9}+\frac {20}{27}+{\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{-x}+c_3 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 42

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

\[ y(x)\to \frac {1}{27} \left (9 x^2+6 x+20\right )+c_1 e^{-x}+c_2 e^x+c_3 e^{3 x} \]