Internal problem ID [10819]
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. Equations
of the form \((g_1(x)+g_0(x))y'=f_2(x) y^2+f_1(x) y+f_0(x)\)
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (y+a x +b \right ) y^{\prime }-\alpha y=\beta x +\gamma } \]
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 211
dsolve((y(x)+a*x+b)*diff(y(x),x)=alpha*y(x)+beta*x+gamma,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (a x +b \right ) \alpha -x \beta -\gamma \right ) \sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }\, \tan \left (\operatorname {RootOf}\left (-2 \sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }\, \ln \left (2\right )+\sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }\, \ln \left (-\sec \left (\textit {\_Z} \right )^{2} \left (a^{2}-2 a \alpha +\alpha ^{2}+4 \beta \right ) \left (a \alpha x +b \alpha -x \beta -\gamma \right )^{2}\right )+2 c_{1} \sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }+2 \textit {\_Z} a +2 \textit {\_Z} \alpha \right )\right )+\left (a x +b \right ) \alpha ^{2}+\left (-a^{2} x -a b -x \beta -\gamma \right ) \alpha +\left (x \beta -\gamma \right ) a +2 b \beta }{2 a \alpha -2 \beta } \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y[x]*a*x+b)*y'[x]==\[Alpha]*y[x]+\[Beta]*x+\[Gamma],y[x],x,IncludeSingularSolutions -> True]
Not solved