59.1.573 problem 589

Internal problem ID [9745]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 589
Date solved : Monday, January 27, 2025 at 06:13:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 19

dsolve(9*x^2*diff(y(x),x$2)+3*x*(1-x^2)*diff(y(x),x)+(1+7*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = -\frac {x^{{1}/{3}} \left (x^{2}-6\right ) \left (c_{1} -c_{2} \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.364 (sec). Leaf size: 59

DSolve[9*x^2*D[y[x],{x,2}]+3*x*(1-x^2)*D[y[x],x]+(1+7*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt [3]{e} \sqrt [3]{x} \left (x^2-6\right ) \left (c_2 \int _1^x\frac {e^{\frac {K[1]^2}{6}-1}}{K[1] \left (K[1]^2-6\right )^2}dK[1]+c_1\right ) \]