Internal problem ID [11056]
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: 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y=0} \]
✗ Solution by Maple
dsolve((x^2+a)^2*diff(y(x),x$2)+b*x^n*(x^2+a)*diff(y(x),x)-m*(b*x^(n+1)+(m-1)*x^2+a)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(x^2+a)^2*y''[x]+b*x^n*(x^2+a)*y'[x]-m*(b*x^(n+1)+(m-1)*x^2+a)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved