Internal problem ID [11067]
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: 243.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y=0} \]
✓ Solution by Maple
Time used: 0.375 (sec). Leaf size: 56
dsolve(x^n*diff(y(x),x$2)+(a*x+b)*diff(y(x),x)-a*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\left (c_{1} \left (\int \frac {{\mathrm e}^{\frac {x^{-n +1} \left (a x \left (n -1\right )+b \left (n -2\right )\right )}{\left (n -2\right ) \left (n -1\right )}}}{\left (a x +b \right )^{2}}d x \right )+c_{2} \right ) \left (a x +b \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^n*y''[x]+(a*x+b)*y'[x]-a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved