Internal problem ID [11008]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-5 Equation of form
\((a x^2+b x+c) y''+f(x)y'+g(x)y=0\)
Problem number: 174.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {\left (2 a x +x^{2}+b \right ) y^{\prime \prime }+\left (x +a \right ) y^{\prime }-y m^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve((x^2+2*a*x+b)*diff(y(x),x$2)+(x+a)*diff(y(x),x)-m^2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x +a +\sqrt {2 a x +x^{2}+b}\right )^{-m}+c_{2} \left (x +a +\sqrt {2 a x +x^{2}+b}\right )^{m} \]
✓ Solution by Mathematica
Time used: 0.301 (sec). Leaf size: 63
DSolve[(x^2+2*a*x+b)*y''[x]+(x+a)*y'[x]-m^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cosh \left (m \log \left (\sqrt {2 a x+b+x^2}-a-x\right )\right )-i c_2 \sinh \left (m \log \left (\sqrt {2 a x+b+x^2}-a-x\right )\right ) \]