62.38.5 problem Ex 5

Internal problem ID [13016]
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 62. Summary. Page 144
Problem number : Ex 5
Date solved : Tuesday, January 28, 2025 at 04:49:17 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve((x^2-x)*diff(y(x),x$2)+(4*x+2)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {12 x^{3} c_{1} \ln \left (x \right )+\left (-3 x^{4}+18 x^{2}-6 x +1\right ) c_{1} +c_{2} x^{3}}{\left (x -1\right )^{5}} \]

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 93

DSolve[(x^2-x)*D[y[x],{x,2}]+(4*x+2)*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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