29.4.12 problem 101

Internal problem ID [4703]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 101
Date solved : Sunday, March 30, 2025 at 03:42:40 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }+x^{3}&=x \sqrt {x^{4}+4 y} \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 47

ode:=diff(y(x),x)+x^3 = x*(x^4+4*y(x))^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\left (y-c_1 \right ) \sqrt {x^{4}+4 y}-x^{2} \left (c_1 +y\right )}{x^{2}+\sqrt {x^{4}+4 y}} = 0 \]

✓ Mathematica. Time used: 1.786 (sec). Leaf size: 68

ode=D[y[x],x]+x^3==x Sqrt[x^4+4 y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to (\cosh (2 c_1)+\sinh (2 c_1)) \left (-x^2+\cosh (2 c_1)+\sinh (2 c_1)\right ) \\ y(x)\to (\cosh (2 c_1)+\sinh (2 c_1)) \left (x^2+\cosh (2 c_1)+\sinh (2 c_1)\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.895 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3 - x*sqrt(x**4 + 4*y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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