61.25.2 problem 2

Internal problem ID [12495]
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 1.3.4-2.
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 03:17:53 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y+a x +b \right ) y^{\prime }&=\alpha y+\beta x +\gamma \end{align*}

✓ Solution by Maple

Time used: 0.703 (sec). Leaf size: 211

dsolve((y(x)+a*x+b)*diff(y(x),x)=alpha*y(x)+beta*x+gamma,y(x), singsol=all)
 

\[ y = \frac {\left (\left (a x +b \right ) \alpha -\beta x -\gamma \right ) \sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }\, \tan \left (\operatorname {RootOf}\left (-2 \sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }\, \ln \left (2\right )+\sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }\, \ln \left (-\sec \left (\textit {\_Z} \right )^{2} \left (a^{2}-2 a \alpha +\alpha ^{2}+4 \beta \right ) \left (a \alpha x +b \alpha -\beta x -\gamma \right )^{2}\right )+2 c_{1} \sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }+2 a \textit {\_Z} +2 \textit {\_Z} \alpha \right )\right )+\left (a x +b \right ) \alpha ^{2}+\left (-a^{2} x -a b -\beta x -\gamma \right ) \alpha +\left (\beta x -\gamma \right ) a +2 b \beta }{2 a \alpha -2 \beta } \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(y[x]*a*x+b)*D[y[x],x]==\[Alpha]*y[x]+\[Beta]*x+\[Gamma],y[x],x,IncludeSingularSolutions -> True]
 

Not solved