76.1.22 problem 22

Internal problem ID [17321]
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 : 22
Date solved : Tuesday, January 28, 2025 at 10:00:04 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2^{{1}/{3}} \end{align*}

✓ Solution by Maple

Time used: 1.037 (sec). Leaf size: 27

dsolve([diff(y(x),x)=x*(x^2+1)/6*y(x)^5,y(0) = -2^(1/3)],y(x), singsol=all)
 

\[ y = -\frac {\sqrt {6}}{\left (-6 x^{4}+9 \,2^{{2}/{3}}-12 x^{2}\right )^{{1}/{4}}} \]

✓ Solution by Mathematica

Time used: 0.246 (sec). Leaf size: 36

DSolve[{D[y[x],x]==x*(x^2+1)/6*y[x]^5,{y[0]==-2^(1/3)}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sqrt {2}}{\sqrt [4]{-\frac {2 x^4}{3}-\frac {4 x^2}{3}+2^{2/3}}} \]