Internal problem ID [9227]
Internal file name [OUTPUT/8163_Monday_June_06_2022_01_59_45_AM_31358032/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 894.
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]
Unable to solve or complete the solution.
\[ \boxed {y^{\prime }+\frac {i \left (i x +1+x^{4}+2 y^{2} x^{2}+y^{4}+x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4}+y^{6}\right )}{y}=0} \] Unable to determine ODE type.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & \mathrm {I} y^{6}+3 \,\mathrm {I} x^{2} y^{4}+3 \,\mathrm {I} x^{4} y^{2}+\mathrm {I} x^{6}+\mathrm {I} y^{4}+2 \,\mathrm {I} y^{2} x^{2}+\mathrm {I} x^{4}-x +y^{\prime } y+\mathrm {I}=0 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=\frac {-\mathrm {I} y^{6}-3 \,\mathrm {I} x^{2} y^{4}-3 \,\mathrm {I} x^{4} y^{2}-\mathrm {I} x^{6}-\mathrm {I} y^{4}-2 \,\mathrm {I} y^{2} x^{2}-\mathrm {I} x^{4}+x -\mathrm {I}}{y} \end {array} \]
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 Looking for potential symmetries trying inverse_Riccati trying an equivalence to an Abel ODE differential order: 1; trying a linearization to 2nd order --- trying a change of variables {x -> y(x), y(x) -> x} differential order: 1; trying a linearization to 2nd order trying 1st order ODE linearizable_by_differentiation --- Trying Lie symmetry methods, 1st order --- `, `-> Computing symmetries using: way = 2 `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = 4 trying symmetry patterns for 1st order ODEs -> trying a symmetry pattern of the form [F(x)*G(y), 0] -> trying a symmetry pattern of the form [0, F(x)*G(y)] -> trying symmetry patterns of the forms [F(x),G(y)] and [G(y),F(x)] -> trying a symmetry pattern of the form [F(x),G(x)] -> trying a symmetry pattern of the form [F(y),G(y)] -> trying a symmetry pattern of the form [F(x)+G(y), 0] -> trying a symmetry pattern of the form [0, F(x)+G(y)] -> trying a symmetry pattern of the form [F(x),G(x)*y+H(x)] -> trying a symmetry pattern of conformal type`
✗ Solution by Maple
dsolve(diff(y(x),x) = -I*(I*x+1+x^4+2*x^2*y(x)^2+y(x)^4+x^6+3*x^4*y(x)^2+3*x^2*y(x)^4+y(x)^6)/y(x),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x] == ((-I)*(1 + I*x + x^4 + x^6 + 2*x^2*y[x]^2 + 3*x^4*y[x]^2 + y[x]^4 + 3*x^2*y[x]^4 + y[x]^6))/y[x],y[x],x,IncludeSingularSolutions -> True]
Not solved