28.1.124 problem 147

Internal problem ID [4430]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 147
Date solved : Tuesday, March 04, 2025 at 06:43:14 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} 2 x^{{3}/{2}}+x^{2}+y^{2}+2 y \sqrt {x}\, y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 41

ode:=2*x^(3/2)+x^2+y(x)^2+2*y(x)*x^(1/2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{-2 \sqrt {x}} c_{1} -x^{2}} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{-2 \sqrt {x}} c_{1} -x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 3.934 (sec). Leaf size: 55

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

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

✓ Sympy. Time used: 0.842 (sec). Leaf size: 39

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

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