59.1.540 problem 556

Internal problem ID [9712]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 556
Date solved : Monday, January 27, 2025 at 06:13:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 24

dsolve(4*x^2*(3+2*x+x^2)*diff(y(x),x$2)-x*(3-14*x-15*x^2)*diff(y(x),x)+(3+7*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} x^{{1}/{4}}+c_{1} x}{x^{2}+2 x +3} \]

✓ Solution by Mathematica

Time used: 0.272 (sec). Leaf size: 67

DSolve[4*x^2*(3+2*x+x^2)*D[y[x],{x,2}]-x*(3-14*x-15*x^2)*D[y[x],x]+(3+7*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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