34.30 problem 30

Internal problem ID [11118]

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: 30.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

\[ \boxed {y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+{\mathrm e}^{\mu x} b \right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left ({\mathrm e}^{\mu x} b +\lambda \right ) y=0} \]

✗ Solution by Maple

dsolve(diff(y(x),x$2)+(a*exp(lambda*x)+b*exp(mu*x))*diff(y(x),x)+a*exp(lambda*x)*(b*exp(mu*x)+lambda)*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[y''[x]+(a*Exp[\[Lambda]*x]+b*Exp[\[Mu]*x])*y'[x]+a*Exp[\[Lambda]*x]*(b*Exp[\[Mu]*x]+\[Lambda])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved