59.1.594 problem 610

Internal problem ID [9766]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 610
Date solved : Monday, January 27, 2025 at 06:14:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 50

dsolve(x^2*(1+2*x)*diff(y(x),x$2)+x*(9+13*x)*diff(y(x),x)+(7+5*x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {280 c_{2} \left (x +\frac {1}{2}\right )^{3} \left (x^{3}-\frac {9}{7} x^{2}+\frac {36}{35} x -\frac {4}{7}\right ) \sqrt {2 x +1}+143 c_{1} x^{2}+104 c_{1} x +20 c_{1}}{x^{7}} \]

✓ Solution by Mathematica

Time used: 0.540 (sec). Leaf size: 141

DSolve[x^2*(1+2*x)*D[y[x],{x,2}]+x*(9+13*x)*D[y[x],x]+(7+5*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{143} \left (143 x^2+104 x+20\right ) \exp \left (\int _1^x-\frac {15 K[1]+5}{4 K[1]^2+2 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {13 K[2]+9}{2 K[2]^2+K[2]}dK[2]\right ) \left (c_2 \int _1^x\frac {20449 \exp \left (-2 \int _1^{K[3]}-\frac {15 K[1]+5}{4 K[1]^2+2 K[1]}dK[1]\right )}{\left (143 K[3]^2+104 K[3]+20\right )^2}dK[3]+c_1\right ) \]