61.32.4 problem 214

Internal problem ID [12714]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-7
Problem number : 214
Date solved : Tuesday, January 28, 2025 at 04:16:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 43

dsolve(x^4*diff(y(x),x$2)+2*x^2*(x+a)*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 51

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

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