61.33.2 problem 239

Internal problem ID [12740]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-8. Other equations.
Problem number : 239
Date solved : Tuesday, January 28, 2025 at 04:17:25 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{6} y^{\prime \prime }+\left (3 x^{2}+a \right ) x^{3} y^{\prime }+b y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 45

dsolve(x^6*diff(y(x),x$2)+(3*x^2+a)*x^3*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-\frac {-a +\sqrt {a^{2}-4 b}}{4 x^{2}}}+c_{2} {\mathrm e}^{\frac {a +\sqrt {a^{2}-4 b}}{4 x^{2}}} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 56

DSolve[x^6*D[y[x],{x,2}]+(3*x^2+a)*x^3*D[y[x],x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{\frac {a-\sqrt {a^2-4 b}}{4 x^2}} \left (c_1 e^{\frac {\sqrt {a^2-4 b}}{2 x^2}}+c_2\right ) \]