Internal problem ID [9702]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.3-2. Equations with power and
exponential functions
Problem number: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}-2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}+a^{2} {\mathrm e}^{2 \lambda \,x^{2}}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)=y(x)^2+2*a*lambda*x*exp(lambda*x^2)-a^2*exp(2*lambda*x^2),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==y[x]^2+2*a*\[Lambda]*x*Exp[\[Lambda]*x^2]-a^2*Exp[2*\[Lambda]*x^2],y[x],x,IncludeSingularSolutions -> True]
Not solved