62.35.1 problem Ex 1

Internal problem ID [12997]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 59. Linear equations with particular integral known. Page 136
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 08:24:45 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 17

dsolve((x^2-2*x+2)*diff(y(x),x$3)-x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} x +c_{2} x^{2}+c_{3} {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 80

DSolve[(x^2-2*x+2)*D[y[x],{x,3}]-x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x \left (2 c_3 \int _1^x\frac {1}{2} \int \exp \left (\int _1^{K[2]}\frac {K[1]^3-3 K[1]^2+6 K[1]-6}{K[1] \left (K[1]^2-2 K[1]+2\right )}dK[1]\right ) \, dK[2]dK[2]+c_2 x+2 c_1\right ) \]