76.1.2 problem 2

Internal problem ID [17301]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 09:59:05 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 43

dsolve(diff(y(x),x)=x^2/y(x)*(1+x^3),y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {3 x^{6}+6 x^{3}+9 c_{1}}}{3} \\ y &= \frac {\sqrt {3 x^{6}+6 x^{3}+9 c_{1}}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 56

DSolve[D[y[x],x]==x^2/y[x]*(1+x^3),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x^6+2 x^3+6 c_1}}{\sqrt {3}} \\ y(x)\to \frac {\sqrt {x^6+2 x^3+6 c_1}}{\sqrt {3}} \\ \end{align*}