Internal problem ID [5089]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (1+y\right )^{2} y^{\prime }=-x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 89
dsolve(x^3+(y(x)+1)^2*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (-6 x^{4}-24 c_{1} \right )^{\frac {1}{3}}}{2}-1 \\ y \left (x \right ) &= -\frac {\left (-6 x^{4}-24 c_{1} \right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, \left (-6 x^{4}-24 c_{1} \right )^{\frac {1}{3}}}{4}-1 \\ y \left (x \right ) &= -\frac {\left (-6 x^{4}-24 c_{1} \right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, \left (-6 x^{4}-24 c_{1} \right )^{\frac {1}{3}}}{4}-1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.483 (sec). Leaf size: 110
DSolve[x^3+(y[x]+1)^2*y'[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*}