59.1.731 problem 748

Internal problem ID [9903]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 748
Date solved : Monday, January 27, 2025 at 06:15:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

dsolve(x^2*(1+x)*diff(y(x),x$2)-(1+2*x)*(x*diff(y(x),x)-y(x))=0,y(x), singsol=all)
 

\[ y = x \left (c_{2} \ln \left (x \right )+c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.183 (sec). Leaf size: 132

DSolve[x^2*(1+x)*D[y[x],{x,2}]-(1+2*x)*(x*D[y[x],x]+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^{1+\sqrt {2}} \operatorname {Hypergeometric2F1}\left (-\frac {1}{2}+\sqrt {2}-\frac {\sqrt {17}}{2},-\frac {1}{2}+\sqrt {2}+\frac {\sqrt {17}}{2},1+2 \sqrt {2},-x\right )+c_1 x^{1-\sqrt {2}} \operatorname {Hypergeometric2F1}\left (\frac {1}{2} \left (-1-2 \sqrt {2}-\sqrt {17}\right ),\frac {1}{2} \left (-1-2 \sqrt {2}+\sqrt {17}\right ),1-2 \sqrt {2},-x\right ) \]