Internal problem ID [1007]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{3}+2 x y^{2}+y x^{2}+x^{3}}{x \left (x +y\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 96
dsolve(diff(y(x),x)=(y(x)^3+2*x*y(x)^2+x^2*y(x)+x^3)/(x*(y(x)+x)^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (3 \ln \relax (x )+3 c_{1}\right )^{\frac {1}{3}} x -x \\ y \relax (x ) = \left (-\frac {\left (3 \ln \relax (x )+3 c_{1}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (3 \ln \relax (x )+3 c_{1}\right )^{\frac {1}{3}}}{2}\right ) x -x \\ y \relax (x ) = \left (-\frac {\left (3 \ln \relax (x )+3 c_{1}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (3 \ln \relax (x )+3 c_{1}\right )^{\frac {1}{3}}}{2}\right ) x -x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.863 (sec). Leaf size: 109
DSolve[y'[x]==(y[x]^3+2*x*y[x]^2+x^2*y[x]+x^3)/(x*(y[x]+x)^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\sqrt [3]{x^3 (3 \log (x)+1+3 c_1)} \\ y(x)\to -x+\frac {1}{2} i \left (\sqrt {3}+i\right ) \sqrt [3]{x^3 (3 \log (x)+1+3 c_1)} \\ y(x)\to -x-\frac {1}{2} \left (1+i \sqrt {3}\right ) \sqrt [3]{x^3 (3 \log (x)+1+3 c_1)} \\ \end{align*}