Internal problem ID [11048]
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 Equation of form
\((a_4 x^4+a_3 x^3+a_2 x^2 x+a_1 x+a_0) y''+f(x)y'+g(x)y=0\)
Problem number: 214.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{4} y^{\prime \prime }+2 \left (x +a \right ) y^{\prime } x^{2}+b y=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {a -\sqrt {a^{2}-b}}{x}}+c_{2} {\mathrm e}^{\frac {a +\sqrt {a^{2}-b}}{x}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 51
DSolve[x^4*y''[x]+2*x^2*(x+a)*y'[x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{\frac {a-\sqrt {a^2-b}}{x}} \left (c_1 e^{\frac {2 \sqrt {a^2-b}}{x}}+c_2\right ) \]