Internal problem ID [10783]
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`]]
\[ \boxed {y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}}=\frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 169
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)
\[ c_{1} -\frac {4^{\frac {1}{3}} 27^{\frac {2}{3}} 5^{\frac {1}{6}} \left (x -\frac {3}{4}\right ) \sqrt {\frac {y \left (x \right ) x^{2}+a -\frac {a}{x}}{y \left (x \right ) x^{2}+a}}}{5 x \left (\frac {3 y \left (x \right ) x^{2}+3 a -\frac {a}{x}}{y \left (x \right ) x^{2}+a}\right )^{\frac {1}{6}} {\left (\frac {a}{x \left (-y \left (x \right ) x^{2}-a \right )}\right )}^{\frac {1}{3}}}-\left (\int _{}^{\frac {\frac {9 y \left (x \right ) x^{3}}{5}+\frac {9 a x}{5}-\frac {27 a}{20}}{x \left (y \left (x \right ) x^{2}+a \right )}}\frac {\textit {\_a} \sqrt {20 \textit {\_a} -9}}{\left (9+4 \textit {\_a} \right )^{\frac {1}{6}} \left (5 \textit {\_a} -9\right )^{\frac {1}{3}} \left (\frac {400}{729} \textit {\_a}^{3}-\frac {7}{3} \textit {\_a} +1\right )}d \textit {\_a} \right ) = 0 \]
✗ 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