59.1.62 problem 64

Internal problem ID [9234]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 64
Date solved : Monday, January 27, 2025 at 05:52:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 65

dsolve((2*x^2+4*x+5)*diff(y(x),x$2)-20*(x+1)*diff(y(x),x)+60*y(x)=0,y(x), singsol=all)
 

\[ y = c_{2} x^{6}+c_{1} x^{5}+\frac {5 \left (2 c_{1} -15 c_{2} \right ) x^{4}}{2}+5 \left (c_{1} -20 c_{2} \right ) x^{3}+\frac {5 \left (-4 c_{1} -45 c_{2} \right ) x^{2}}{4}+\frac {\left (-31 c_{1} +120 c_{2} \right ) x}{4}-\frac {7 c_{1}}{4}+\frac {155 c_{2}}{8} \]

✓ Solution by Mathematica

Time used: 0.582 (sec). Leaf size: 108

DSolve[(2*x^2+4*x+5)*D[y[x],{x,2}]-20*(x+1)*D[y[x],x]+60*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (2 x^2+4 x+5\right )^{5/2} \exp \left (\int _1^x\frac {2 \left (K[1]+3 i \sqrt {6}+1\right )}{2 K[1] (K[1]+2)+5}dK[1]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}\frac {2 \left (K[1]+3 i \sqrt {6}+1\right )}{2 K[1] (K[1]+2)+5}dK[1]\right )dK[2]+c_1\right ) \]