Internal problem ID [10829]
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: 0.672 (sec). Leaf size: 186
dsolve((y(x)+a*x+b)*diff(y(x),x)=alpha*y(x)+beta*x+gamma,y(x), singsol=all)
\[ y \left (x \right ) = \frac {a \gamma -b \beta -\frac {\left (x \left (a \alpha -\beta \right )+b \alpha -\gamma \right ) \left (\tan \left (\operatorname {RootOf}\left (\sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }\, \ln \left (-\frac {\left (x \left (a \alpha -\beta \right )+b \alpha -\gamma \right )^{2} \left (\tan \left (\textit {\_Z} \right )^{2} a^{2}-2 \tan \left (\textit {\_Z} \right )^{2} a \alpha +\alpha ^{2} \tan \left (\textit {\_Z} \right )^{2}+4 \tan \left (\textit {\_Z} \right )^{2} \beta +a^{2}-2 a \alpha +\alpha ^{2}+4 \beta \right )}{4}\right )+2 c_{1} \sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }+2 a \textit {\_Z} +2 \textit {\_Z} \alpha \right )\right ) \sqrt {-a^{2}+2 a \alpha -\alpha ^{2}-4 \beta }-a +\alpha \right )}{2}}{-a \alpha +\beta } \]
✗ 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