Internal problem ID [9680]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.3. Equations Containing Exponential
Functions
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-a \,{\mathrm e}^{\mu x} y^{2}-a b \,{\mathrm e}^{x \left (\lambda +\mu \right )} y+b \lambda \,{\mathrm e}^{\lambda x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 1648
dsolve(diff(y(x),x)=a*exp(mu*x)*y(x)^2+a*b*exp((lambda+mu)*x)*y(x)-b*lambda*exp(lambda*x),y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 10.068 (sec). Leaf size: 1184
DSolve[y'[x]==a*Exp[\[Mu]*x]*y[x]^2+a*b*Exp[(\[Lambda]+\[Mu])*x]*y[x]-b*\[Lambda]*Exp[\[Lambda]*x],y[x],x,IncludeSingularSolutions -> True]
Too large to display