59.1.96 problem 98

Internal problem ID [9268]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 98
Date solved : Monday, January 27, 2025 at 06:00:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.113 (sec). Leaf size: 41

dsolve(x^2*(3+4*x)*diff(y(x),x$2)+x*(11+4*x)*diff(y(x),x)-(3+4*x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \left (48 x^{2}+32 x +7\right )}{x^{3}}+c_{2} \operatorname {hypergeom}\left (\left [3, 5\right ], \left [\frac {13}{3}\right ], -\frac {4 x}{3}\right ) \left (4 x +3\right )^{{11}/{3}} x^{{1}/{3}} \]

✓ Solution by Mathematica

Time used: 0.809 (sec). Leaf size: 143

DSolve[x^2*(3+4*x)*D[y[x],{x,2}]+x*(11+4*x)*D[y[x],x]-(3+4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{48} \left (48 x^2+32 x+7\right ) \exp \left (\int _1^x-\frac {20 K[1]+7}{8 K[1]^2+6 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {4 K[2]+11}{4 K[2]^2+3 K[2]}dK[2]\right ) \left (c_2 \int _1^x\frac {2304 \exp \left (-2 \int _1^{K[3]}-\frac {20 K[1]+7}{8 K[1]^2+6 K[1]}dK[1]\right )}{\left (48 K[3]^2+32 K[3]+7\right )^2}dK[3]+c_1\right ) \]