60.2.282 problem 859

Internal problem ID [10856]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 859
Date solved : Sunday, March 30, 2025 at 07:16:15 PM
CAS classification : [NONE]

\begin{align*} y^{\prime }&=-\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \end{align*}

✓ Maple. Time used: 0.078 (sec). Leaf size: 63

ode:=diff(y(x),x) = -(-x-_F1(y(x)^2-2*x))/(y(x)^2)^(1/2)/x; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {2 \operatorname {RootOf}\left (\ln \left (x \right )-\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (2 \textit {\_a} \right )}d \textit {\_a} +2 c_1 \right )+2 x} \\ y &= -\sqrt {2 \operatorname {RootOf}\left (\ln \left (x \right )-\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (2 \textit {\_a} \right )}d \textit {\_a} +2 c_1 \right )+2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.349 (sec). Leaf size: 101

ode=D[y[x],x] == (x + F1[-2*x + y[x]^2])/(x*Sqrt[y[x]^2]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {\sqrt {K[2]^2}}{\text {F1}\left (K[2]^2-2 x\right )}-\int _1^x\frac {2 K[2] \text {F1}''\left (K[2]^2-2 K[1]\right )}{\text {F1}\left (K[2]^2-2 K[1]\right )^2}dK[1]\right )dK[2]+\int _1^x\left (-\frac {1}{K[1]}-\frac {1}{\text {F1}\left (y(x)^2-2 K[1]\right )}\right )dK[1]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
F1 = Function("F1") 
ode = Eq(Derivative(y(x), x) + (-x - F1(-2*x + y(x)**2))/(x*sqrt(y(x)**2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x + F1(-2*x + y(x)**2))*sqrt(y(x)**2)/(x*y(x)**2) cannot be solved by the factorable group method