38.2.3 problem 3

Internal problem ID [6432]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 3
Date solved : Wednesday, March 05, 2025 at 12:41:38 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 87

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

\begin{align*} y &= \frac {\left (-6 x^{4}-24 c_1 \right )^{{1}/{3}}}{2}-1 \\ y &= -\frac {\left (-6 x^{4}-24 c_1 \right )^{{1}/{3}}}{4}-\frac {i \sqrt {3}\, \left (-6 x^{4}-24 c_1 \right )^{{1}/{3}}}{4}-1 \\ y &= -\frac {\left (-6 x^{4}-24 c_1 \right )^{{1}/{3}}}{4}+\frac {i \sqrt {3}\, \left (-6 x^{4}-24 c_1 \right )^{{1}/{3}}}{4}-1 \\ \end{align*}

✓ Mathematica. Time used: 0.496 (sec). Leaf size: 110

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

\begin{align*} y(x)\to -1+\frac {\sqrt [3]{-3 x^4+4+12 c_1}}{2^{2/3}} \\ y(x)\to -1+\frac {i \left (\sqrt {3}+i\right ) \sqrt [3]{-3 x^4+4+12 c_1}}{2\ 2^{2/3}} \\ y(x)\to -1-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-3 x^4+4+12 c_1}}{2\ 2^{2/3}} \\ \end{align*}

✓ Sympy. Time used: 1.500 (sec). Leaf size: 105

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt [3]{3 C_{1} - \frac {3 x^{4}}{4} + 1}}{2} - \frac {\sqrt {3} i \sqrt [3]{3 C_{1} - \frac {3 x^{4}}{4} + 1}}{2} - 1, \ y{\left (x \right )} = - \frac {\sqrt [3]{3 C_{1} - \frac {3 x^{4}}{4} + 1}}{2} + \frac {\sqrt {3} i \sqrt [3]{3 C_{1} - \frac {3 x^{4}}{4} + 1}}{2} - 1, \ y{\left (x \right )} = \sqrt [3]{C_{1} - \frac {3 x^{4}}{4}} - 1\right ] \]