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 : Monday, January 27, 2025 at 02:02:51 PM
CAS classification : [_separable]

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

✓ Solution by Maple

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

dsolve(x^3+(y(x)+1)^2*diff(y(x),x)=0,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*}

✓ Solution by Mathematica

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

DSolve[x^3+(y[x]+1)^2*D[y[x],x]==0,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*}