85.33.34 problem 34

Internal problem ID [22657]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 34
Date solved : Thursday, October 02, 2025 at 09:03:01 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 37

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

\begin{align*} y &= \frac {c_1}{4}-\frac {\sqrt {c_1^{2}-8 x}}{4} \\ y &= \frac {c_1}{4}+\frac {\sqrt {c_1^{2}-8 x}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.175 (sec). Leaf size: 54

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

\begin{align*} y(x)&\to \frac {1}{4} \left (c_1-\sqrt {-8 x+c_1{}^2}\right )\\ y(x)&\to \frac {1}{4} \left (\sqrt {-8 x+c_1{}^2}+c_1\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.436 (sec). Leaf size: 36

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

\[ \left [ y{\left (x \right )} = - \frac {C_{1}}{4} - \frac {\sqrt {C_{1}^{2} - 8 x}}{4}, \ y{\left (x \right )} = - \frac {C_{1}}{4} + \frac {\sqrt {C_{1}^{2} - 8 x}}{4}\right ] \]