Internal problem ID [11077]
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]]
\[ \boxed {x^{n} y^{\prime \prime }+y^{\prime } \left (a x +b \right )-a y=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 95
dsolve(x^n*diff(y(x),x$2)+(a*x+b)*diff(y(x),x)-a*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -c_{1} \left (\int \frac {{\mathrm e}^{\left (\frac {a \,x^{2}}{n -2}+\frac {b x}{n -1}\right ) x^{-n}}}{\left (a x +b \right )^{2}}d x \right ) x a -c_{1} \left (\int \frac {{\mathrm e}^{\left (\frac {a \,x^{2}}{n -2}+\frac {b x}{n -1}\right ) x^{-n}}}{\left (a x +b \right )^{2}}d x \right ) b -c_{2} x a -c_{2} b \]
✗ 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