85.34.11 problem 11

Internal problem ID [22719]
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. B Exercises at page 67
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:13:02 PM
CAS classification : [_rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 15

ode:=diff(y(x),x) = 1/2*(x+y(x)^2)/y(x); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sqrt {2 \,{\mathrm e}^{x}-x -1} \]

✓ Mathematica. Time used: 2.475 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.314 (sec). Leaf size: 14

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

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