Internal problem ID [10779]
Internal file name [OUTPUT/9727_Monday_June_06_2022_04_48_00_PM_3906511/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: 43.
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.
\[ \boxed {y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{\frac {6}{5}}}=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{\frac {7}{5}}}} \] Unable to determine ODE type.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & 30 y y^{\prime } x^{\frac {7}{5}}+33 a y x^{\frac {6}{5}}+9 a^{2} x^{2}+2 a y x^{\frac {1}{5}}-13 a^{2} x +4 a^{2}=0 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=\frac {-33 a y x^{\frac {6}{5}}-9 a^{2} x^{2}-2 a y x^{\frac {1}{5}}+13 a^{2} x -4 a^{2}}{30 y x^{\frac {7}{5}}} \end {array} \]
Maple trace
`Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear trying Bernoulli trying separable trying inverse linear trying homogeneous types: trying Chini differential order: 1; looking for linear symmetries trying exact trying Abel Looking for potential symmetries Looking for potential symmetries <- Abel successful`
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 4330
dsolve(y(x)*diff(y(x),x)+1/30*a*(33*x+2)*x^(-6/5)*y(x)=-1/30*a^2*(x-1)*(9*x-4)*x^(-7/5),y(x), singsol=all)
\[ \text {Expression too large to display} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]+1/30*a*(33*x+2)*x^(-6/5)*y[x]==-1/30*a^2*(x-1)*(9*x-4)*x^(-7/5),y[x],x,IncludeSingularSolutions -> True]
Timed out