29.35.26 problem 1060

Internal problem ID [5624]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1060
Date solved : Sunday, March 30, 2025 at 09:21:53 AM
CAS classification : [_quadrature]

\begin{align*} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=x*diff(y(x),x)^3-(x+x^2+y(x))*diff(y(x),x)^2+(x^2+y(x)+x*y(x))*diff(y(x),x)-x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 x \\ y &= x +c_1 \\ y &= \frac {x^{2}}{2}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 36

ode=x (D[y[x],x])^3 - (x+x^2+y[x])(D[y[x],x])^2 + (x^2+y[x]+x y[x]) D[y[x],x]-x y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 x \\ y(x)\to x+c_1 \\ y(x)\to \frac {x^2}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.217 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + x*Derivative(y(x), x)**3 - (x**2 + x + y(x))*Derivative(y(x), x)**2 + (x**2 + x*y(x) + y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} + x, \ y{\left (x \right )} = C_{1} + \frac {x^{2}}{2}, \ y{\left (x \right )} = C_{1} x\right ] \]