Internal problem ID [10791]
Internal file name [OUTPUT/9739_Monday_June_06_2022_04_48_39_PM_54450107/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: 55.
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.
\[ \boxed {y y^{\prime }-\frac {3 a y}{x^{\frac {7}{4}}}=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{\frac {5}{2}}}} \] Unable to determine ODE type.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & 4 y y^{\prime } x^{\frac {17}{4}}-x^{\frac {15}{4}} a^{2}+10 x^{\frac {11}{4}} a^{2}-9 a^{2} x^{\frac {7}{4}}-12 x^{\frac {5}{2}} y a =0 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=\frac {x^{\frac {15}{4}} a^{2}-10 x^{\frac {11}{4}} a^{2}+9 a^{2} x^{\frac {7}{4}}+12 x^{\frac {5}{2}} y a}{4 y x^{\frac {17}{4}}} \end {array} \]
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-3*a*x^(-7/4)*y(x)=1/4*a^2*(x-1)*(x-9)*x^(-5/2),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-3*a*x^(-7/4)*y[x]==1/4*a^2*(x-1)*(x-9)*x^(-5/2),y[x],x,IncludeSingularSolutions -> True]
Not solved