Internal problem ID [9963]
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. Form \(y y'-y=f(x)\). subsection 1.3.1-2. Solvable
equations and their solutions
Problem number: 57.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime } y-y+\frac {10 x}{49}-\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 204
dsolve(y(x)*diff(y(x),x)-y(x)=-10/49*x+2/49*A*(4*x^(1/2)+61*A+12*A^2*x^(-1/2)),y(x), singsol=all)
\[ c_{1}-\frac {3 y \relax (x ) \left (A +\frac {\sqrt {x}}{3}\right ) \left (\frac {3 A^{2}+16 A \sqrt {x}+5 x -7 y \relax (x )}{6 A^{2}+2 A \sqrt {x}+y \relax (x )}\right )^{\frac {5}{6}} 2^{\frac {1}{3}}}{\left (\frac {-24 A^{2}-2 A \sqrt {x}+2 x -7 y \relax (x )}{12 A^{2}+4 A \sqrt {x}+2 y \relax (x )}\right )^{\frac {1}{3}} \sqrt {\frac {\left (3 A +\sqrt {x}\right )^{2}}{6 A^{2}+2 A \sqrt {x}+y \relax (x )}}\, \left (12 A^{3}+4 A^{2} \sqrt {x}+2 y \relax (x ) A \right )}-\left (\int _{}^{\frac {6 A \sqrt {x}+2 x -3 y \relax (x )}{12 A^{2}+4 A \sqrt {x}+2 y \relax (x )}}\frac {\left (10 \textit {\_a} +1\right )^{\frac {5}{6}}}{\sqrt {2 \textit {\_a} +3}\, \left (-2+\textit {\_a} \right )^{\frac {1}{3}}}d \textit {\_a} \right ) = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==-10/49*x+2/49*A*(4*x^(1/2)+61*A+12*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
Not solved