29.37.4 problem 1117

Internal problem ID [5662]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1117
Date solved : Tuesday, March 04, 2025 at 11:17:19 PM
CAS classification : [_separable]

\begin{align*} 2 \left (1+y\right )^{{3}/{2}}+3 x y^{\prime }-3 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

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

\[ \ln \left (x \right )+3 \left (\int _{}^{y \left (x \right )}\frac {1}{\left (2 \textit {\_a} +2\right ) \sqrt {\textit {\_a} +1}-3 \textit {\_a}}d \textit {\_a} \right )+c_{1} = 0 \]

✓ Mathematica. Time used: 0.112 (sec). Leaf size: 55

ode=2 (1+y[x])^(3/2) + 3 x D[y[x],x]-3 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{3} \text {RootSum}\left [2 \text {$\#$1}^3-3 \text {$\#$1}^2+3\&,\frac {\log \left (\sqrt {y(x)+1}-\text {$\#$1}\right )}{\text {$\#$1}-1}\&\right ]=-\frac {\log (x)}{3}+c_1,y(x)\right ] \]

✓ Sympy. Time used: 2.985 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*Derivative(y(x), x) + 2*(y(x) + 1)**(3/2) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \int \limits ^{y{\left (x \right )}} \frac {1}{2 y \sqrt {y + 1} - 3 y + 2 \sqrt {y + 1}}\, dy = C_{1} - \frac {\log {\left (x \right )}}{3} \]