59.1.91 problem 93

Internal problem ID [9263]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 93
Date solved : Monday, January 27, 2025 at 06:00:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (1+3 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 41

dsolve(3*x^2*diff(y(x),x$2)+x*(1+x)*diff(y(x),x)-(1+3*x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} {\mathrm e}^{-\frac {x}{3}} \operatorname {hypergeom}\left (\left [3\right ], \left [-\frac {1}{3}\right ], \frac {x}{3}\right )+70 c_{1} \left (x^{{4}/{3}}+\frac {2 x^{{7}/{3}}}{7}+\frac {x^{{10}/{3}}}{70}\right )}{x^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 2.192 (sec). Leaf size: 60

DSolve[3*x^2*D[y[x],{x,2}]+x*(1+x)*D[y[x],x]-(1+3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e x \left (x^2+20 x+70\right ) \left (c_2 \int _1^x\frac {e^{-\frac {K[1]}{3}-\frac {7}{3}}}{K[1]^{7/3} \left (K[1]^2+20 K[1]+70\right )^2}dK[1]+c_1\right ) \]