12.5.46 problem 45

Internal problem ID [1670]
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
Date solved : Monday, January 27, 2025 at 05:24:02 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y y^{\prime }&=3 x^{6}+6 y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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 &= \sqrt {c_1 \,x^{6}-1}\, x^{3} \\ y &= -\sqrt {c_1 \,x^{6}-1}\, x^{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.397 (sec). Leaf size: 42

DSolve[x*y[x]*D[y[x],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*}