4.7 problem 28

Internal problem ID [10436]

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: 28.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }-a \,x^{n} y^{2}=b \lambda \,{\mathrm e}^{\lambda x}-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x}} \]

✗ Solution by Maple

dsolve(diff(y(x),x)=a*x^n*y(x)^2+b*lambda*exp(lambda*x)-a*b^2*x^n*exp(2*lambda*x),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[y'[x]==a*x^n*y[x]^2+b*\[Lambda]*Exp[\[Lambda]*x]-a*b^2*x^n*Exp[2*\[Lambda]*x],y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved