Internal problem ID [9930]
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: 24.
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 {12 x}{49}-\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 274
dsolve(y(x)*diff(y(x),x)-y(x)=-12/49*x+2/49*A*(5*x^(1/2)+34*A+15*A^2*x^(-1/2)),y(x), singsol=all)
\[ \frac {\left (3 A -\sqrt {x}\right ) \left (36 A^{4}+120 A^{3} \sqrt {x}-80 A \,x^{\frac {3}{2}}+52 A^{2} x +84 y \relax (x ) A^{2}+140 A \sqrt {x}\, y \relax (x )+16 x^{2}-56 x y \relax (x )+49 y \relax (x )^{2}\right ) y \relax (x )}{8 \left (\frac {15 A^{2}+4 A \sqrt {x}-3 x +7 y \relax (x )}{6 A^{2}-2 A \sqrt {x}+y \relax (x )}\right )^{\frac {3}{2}} \sqrt {-\frac {\left (3 A -\sqrt {x}\right )^{2}}{6 A^{2}-2 A \sqrt {x}+y \relax (x )}}\, \left (6 A^{2}-2 A \sqrt {x}+y \relax (x )\right )^{3} A}-\frac {\left (54 A^{2}+6 A \sqrt {x}-8 x +21 y \relax (x )\right ) \sqrt {-\frac {2 \left (9 A^{2}-6 A \sqrt {x}+x \right )}{6 A^{2}-2 A \sqrt {x}+y \relax (x )}}\, \sqrt {2}}{12 \left (6 A^{2}-2 A \sqrt {x}+y \relax (x )\right ) \sqrt {\frac {15 A^{2}+4 A \sqrt {x}-3 x +7 y \relax (x )}{6 A^{2}-2 A \sqrt {x}+y \relax (x )}}}+c_{1} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==-12/49*x+2/49*A*(5*x^(1/2)+34*A+15*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
Not solved