Internal problem ID [10030]
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 1.3.3-2. Equations of
the form \(y y'=f_1(x) y+f_0(x)\)
Problem number: 36.
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-\frac {a \left (5 x -4\right ) y}{x^{4}}-\frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 210
dsolve(y(x)*diff(y(x),x)-a*(5*x-4)*x^(-4)*y(x)=a^2*(x-1)*(3*x-1)*x^(-7),y(x), singsol=all)
\[ c_{1}-\frac {\left (4 x -3\right ) 5^{\frac {1}{6}} \sqrt {\frac {x^{2} y \relax (x )}{x^{2} y \relax (x )+a}+\frac {a}{x^{2} y \relax (x )+a}-\frac {a}{x \left (x^{2} y \relax (x )+a \right )}}\, 27^{\frac {2}{3}} 4^{\frac {1}{3}}}{20 x \left (\frac {3 x^{2} y \relax (x )}{x^{2} y \relax (x )+a}+\frac {3 a}{x^{2} y \relax (x )+a}-\frac {a}{x \left (x^{2} y \relax (x )+a \right )}\right )^{\frac {1}{6}} \left (\frac {a}{x \left (-x^{2} y \relax (x )-a \right )}\right )^{\frac {1}{3}}}-\left (\int _{}^{\frac {\frac {9 x^{3} y \relax (x )}{5}+\frac {9 a x}{5}-\frac {27 a}{20}}{x \left (x^{2} y \relax (x )+a \right )}}\frac {\textit {\_a} \sqrt {20 \textit {\_a} -9}}{\left (4 \textit {\_a} +9\right )^{\frac {1}{6}} \left (5 \textit {\_a} -9\right )^{\frac {1}{3}} \left (\frac {400}{729} \textit {\_a}^{3}-\frac {7}{3} \textit {\_a} +1\right )}d \textit {\_a} \right ) = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-a*(5*x-4)*x^(-4)*y[x]==a^2*(x-1)*(3*x-1)*x^(-7),y[x],x,IncludeSingularSolutions -> True]
Not solved