61.34.33 problem 33

Internal problem ID [12797]
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 : 33
Date solved : Tuesday, January 28, 2025 at 04:20:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

dsolve(diff(y(x),x$2)+(a*exp(lambda*x)+b*exp(mu*x)+c)*diff(y(x),x)+(a*b*exp((lambda+mu)*x)+a*c*exp(lambda*x)+b*mu*exp(mu*x))*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]+c)*D[y[x],x]+(a*b*Exp[(\[Lambda]+\[Mu])*x]+a*c*Exp[\[Lambda]*x]+b*\[Mu]*Exp[\[Mu]*x])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved