3.18 problem 18

Internal problem ID [10426]

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: 18.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }-a \,{\mathrm e}^{k x} y^{2}-y b=c \,{\mathrm e}^{k n x}+d \,{\mathrm e}^{k \left (1+2 n \right ) x}} \]

✗ Solution by Maple

dsolve(diff(y(x),x)=a*exp(k*x)*y(x)^2+b*y(x)+c*exp(k*n*x)+d*exp(k*(2*n+1)*x),y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 27.598 (sec). Leaf size: 2503

DSolve[y'[x]==a*Exp[k*x]*y[x]^2+b*y[x]+c*Exp[k*n*x]+d*Exp[k*(2*n+1)*x],y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

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