59.1.591 problem 607

Internal problem ID [9763]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 607
Date solved : Monday, January 27, 2025 at 06:14:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 40

dsolve(4*x^2*(1+x)*diff(y(x),x$2)+4*x*(3+8*x)*diff(y(x),x)-(5-49*x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{3}+6 c_{2} \ln \left (x \right ) x^{3}-18 c_{2} x^{2}-9 c_{2} x -2 c_{2}}{\left (x +1\right )^{4} x^{{5}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.194 (sec). Leaf size: 104

DSolve[4*x^2*(1+x)*D[y[x],{x,2}]+4*x*(3+8*x)*D[y[x],x]-(5-49*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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