Internal problem ID [11069]
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: 245.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{n} y^{\prime \prime }+\left (2 x^{n -1}+a \,x^{2}+b x \right ) y^{\prime }+y b=0} \]
✓ Solution by Maple
Time used: 0.454 (sec). Leaf size: 76
dsolve(x^n*diff(y(x),x$2)+(2*x^(n-1)+a*x^2+b*x)*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (a x +b \right ) \left (c_{2} \left (\int \frac {{\mathrm e}^{\frac {b \left (n -3\right ) x^{2-n}+\left (n -2\right ) \left (a \,x^{3-n}-2 \left (n -3\right ) \ln \left (x \right )\right )}{\left (n -3\right ) \left (n -2\right )}} x^{2}}{\left (a x +b \right )^{2}}d x \right )+c_{1} \right )}{x} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^n*y''[x]+(2*x^(n-1)+a*x^2+b*x)*y'[x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved