61.32.3 problem 213

Internal problem ID [12713]
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 : 213
Date solved : Tuesday, January 28, 2025 at 04:16:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

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

\[ y = x \left ({\mathrm e}^{-\frac {a}{x}} c_{1} +{\mathrm e}^{-\frac {b}{x}} c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 41

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

\[ y(x)\to \frac {c_2 x e^{1-\frac {a}{x}}}{a-b}+c_1 x e^{-\frac {b+x}{x}} \]