77.46.12 problem Ex 12 page 75

Internal problem ID [20861]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter V. Singular solutions
Problem number : Ex 12 page 75
Date solved : Thursday, October 02, 2025 at 06:41:50 PM
CAS classification : [_rational]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 49

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

\begin{align*} y(x)&\to \frac {-c_1 x+1+c_1{}^2}{x+c_1}\\ y(x)&\to -\frac {i}{\sqrt {2}}\\ y(x)&\to \frac {i}{\sqrt {2}} \end{align*}

✗ Sympy

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

Timed Out