59.1.172 problem 174

Internal problem ID [9344]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 174
Date solved : Monday, January 27, 2025 at 06:01:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 65

dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(3+10*x)*diff(y(x),x)+30*x*y(x)=0,y(x), singsol=all)
 

\[ y = 3 c_{2} x^{4} \left (x -\frac {5}{2}\right ) \ln \left (x \right )+\frac {c_{2} x^{6}}{4}+\frac {\left (16 c_{1} -5 c_{2} \right ) x^{5}}{8}+\frac {\left (-80 c_{1} -299 c_{2} \right ) x^{4}}{16}+5 c_{2} x^{3}+\frac {5 c_{2} x^{2}}{4}+\frac {c_{2} x}{4}+\frac {c_{2}}{40} \]

✓ Solution by Mathematica

Time used: 0.518 (sec). Leaf size: 125

DSolve[x^2*(1+x)*D[y[x],{x,2}]-x*(3+10*x)*D[y[x],x]+30*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} (2 x-5) \exp \left (\int _1^x\frac {5-2 K[1]}{2 K[1]^2+2 K[1]}dK[1]-\frac {1}{2} \int _1^x\left (-\frac {7}{K[2]+1}-\frac {3}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\frac {4 \exp \left (-2 \int _1^{K[3]}\frac {5-2 K[1]}{2 K[1]^2+2 K[1]}dK[1]\right )}{(5-2 K[3])^2}dK[3]+c_1\right ) \]