59.1.606 problem 622

Internal problem ID [9778]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 622
Date solved : Monday, January 27, 2025 at 06:14:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 19

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

\[ y = -\frac {x^{2} \left (x^{2}-2\right ) \left (c_{1} -c_{2} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.230 (sec). Leaf size: 50

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

\[ y(x)\to x^2 \left (x^2-2\right ) \left (c_2 \int _1^x\frac {e^{\frac {3 K[1]^2}{2}}}{K[1]^5 \left (K[1]^2-2\right )^2}dK[1]+c_1\right ) \]