Internal problem ID [1000]
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: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{3}+y^{3}}{x y^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 14
dsolve([diff(y(x),x)=(x^3+y(x)^3)/(x*y(x)^2),y(1) = 3],y(x), singsol=all)
\[ y \relax (x ) = \left (3 \ln \relax (x )+27\right )^{\frac {1}{3}} x \]
✓ Solution by Mathematica
Time used: 0.203 (sec). Leaf size: 20
DSolve[{y'[x]==(x^3+y[x]^3)/(x*y[x]^2),y[1]==3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{3} x \sqrt [3]{\log (x)+9} \\ \end{align*}