Internal problem ID [10062]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.3-2. Equations of
the form \(y y'=f_1(x) y+f_0(x)\)
Problem number: 68.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-\left (a \left (\lambda +2 \mu \right ) {\mathrm e}^{\lambda x}+b \right ) {\mathrm e}^{\mu x} y-\left (-a^{2} \mu \,{\mathrm e}^{2 \lambda x}-a \,{\mathrm e}^{\lambda x} b +c \right ) {\mathrm e}^{2 \mu x}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)=(a*(2*mu+lambda)*exp(lambda*x)+b)*exp(mu*x)*y(x)+(-a^2*mu*exp(2*lambda*x)-a*b*exp(lambda*x)+c)*exp(2*mu*x),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]==(a*(2*\[Mu]+\[Lambda])*Exp[\[Lambda]*x]+b)*Exp[\[Mu]*x]*y[x]+(-a^2*\[Mu]*Exp[2*\[Lambda]*x]-a*b*Exp[\[Lambda]*x]+c)*Exp[2*\[Mu]*x],y[x],x,IncludeSingularSolutions -> True]
Not solved