Internal problem ID [11095]
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: 261.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{n} a +b \,x^{m}+c \right ) y^{\prime \prime }+\left (-x +\lambda \right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 157
dsolve((a*x^n+b*x^m+c)*diff(y(x),x$2)+(lambda-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (\int {\mathrm e}^{\int \frac {-2+\frac {x^{2}}{a \,x^{n}+b \,x^{m}+c}-\frac {2 x \lambda }{a \,x^{n}+b \,x^{m}+c}+\frac {\lambda ^{2}}{a \,x^{n}+b \,x^{m}+c}}{-\lambda +x}d x}d x \right ) x -c_{1} \left (\int {\mathrm e}^{\int \frac {-2+\frac {x^{2}}{a \,x^{n}+b \,x^{m}+c}-\frac {2 x \lambda }{a \,x^{n}+b \,x^{m}+c}+\frac {\lambda ^{2}}{a \,x^{n}+b \,x^{m}+c}}{-\lambda +x}d x}d x \right ) \lambda +c_{2} x -c_{2} \lambda \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(a*x^n+b*x^m+c)*y''[x]+(\[Lambda]-x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved