5.46 problem 45

Internal problem ID [1020]

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: 45.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]

Solve \begin {gather*} \boxed {y y^{\prime } x -3 x^{6}-6 y^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 34

dsolve(x*y(x)*diff(y(x),x)=3*x^6+6*y(x)^2,y(x), singsol=all)
 

\begin{align*} y \relax (x ) = \sqrt {x^{6} c_{1}-1}\, x^{3} \\ y \relax (x ) = -\sqrt {x^{6} c_{1}-1}\, x^{3} \\ \end{align*}

Solution by Mathematica

Time used: 0.394 (sec). Leaf size: 42

DSolve[x*y[x]*y'[x]==3*x^6+6*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x^3 \sqrt {-1+c_1 x^6} \\ y(x)\to x^3 \sqrt {-1+c_1 x^6} \\ \end{align*}