29.28.23 problem 821

Internal problem ID [5404]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 821
Date solved : Sunday, March 30, 2025 at 08:10:23 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+2 x y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(y(x),x)^2-(1+2*x*y(x))*diff(y(x),x)+2*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 \,{\mathrm e}^{x^{2}} \\ y &= x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 21

ode=(D[y[x],x])^2-(1+2*x*y[x])*D[y[x],x]+2*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.306 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x) - (2*x*y(x) + 1)*Derivative(y(x), x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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