61.34.30 problem 30

Internal problem ID [12794]
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
Date solved : Tuesday, January 28, 2025 at 04:20:11 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\mu x}+\lambda \right ) y&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],{x,2}]+(a*Exp[\[Lambda]*x]+b*Exp[\[Mu]*x])*D[y[x],x]+a*Exp[\[Lambda]*x]*(b*Exp[\[Mu]*x]+\[Lambda])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved