Internal problem ID [11129]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.3-1. Equations with
exponential functions
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+{\mathrm e}^{x \lambda } \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{x \lambda } \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 93
dsolve(diff(y(x),x$2)+exp(lambda*x)*(a*exp(2*mu*x)+b)*diff(y(x),x)+mu*(exp(lambda*x)*(b-a*exp(2*mu*x))-mu)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (a \,{\mathrm e}^{\mu x}+{\mathrm e}^{-\mu x} b \right )+c_{2} \left (\int \frac {{\mathrm e}^{\frac {-{\mathrm e}^{x \left (\lambda +2 \mu \right )} a \lambda -2 \,{\mathrm e}^{\lambda x} \left (\mu +\frac {\lambda }{2}\right ) b}{\lambda \left (\lambda +2 \mu \right )}}}{\left (a \,{\mathrm e}^{\mu x}+{\mathrm e}^{-\mu x} b \right )^{2}}d x \right ) \left (a \,{\mathrm e}^{\mu x}+{\mathrm e}^{-\mu x} b \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]+Exp[\[Lambda]*x]*(a*Exp[2*\[Mu]*x]+b)*y'[x]+\[Mu]*(Exp[\[Lambda]*x]*(b-a*Exp[2*\[Mu]*x])-\[Mu])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved