Internal problem ID [10758]
Internal file name [OUTPUT/9706_Monday_June_06_2022_03_31_43_PM_93423319/index.tex]
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: 22.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[_rational, [_Abel, `2nd type`, `class B`]]
Unable to solve or complete the solution.
\[ \boxed {y y^{\prime }+\frac {5 a \left (23 x -16\right ) y}{56 x^{\frac {9}{7}}}=-\frac {3 a^{2} \left (x -1\right ) \left (25 x -32\right )}{56 x^{\frac {11}{17}}}} \] Unable to determine ODE type.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & 56 y y^{\prime } x^{\frac {230}{119}}+115 a y x^{\frac {28}{17}}-80 a y x^{\frac {11}{17}}+75 x^{\frac {23}{7}} a^{2}-171 x^{\frac {16}{7}} a^{2}+96 a^{2} x^{\frac {9}{7}}=0 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=\frac {-115 a y x^{\frac {28}{17}}+80 a y x^{\frac {11}{17}}-75 x^{\frac {23}{7}} a^{2}+171 x^{\frac {16}{7}} a^{2}-96 a^{2} x^{\frac {9}{7}}}{56 y x^{\frac {230}{119}}} \end {array} \]
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)+5/56*a*(23*x-16)*x^(-9/7)*y(x)=-3/56*a^2*(x-1)*(25*x-32)*x^(-11/17),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]+5/56*a*(23*x-16)*x^(-9/7)*y[x]==-3/56*a^2*(x-1)*(25*x-32)*x^(-11/17),y[x],x,IncludeSingularSolutions -> True]
Timed out