76.5.2 problem 2

Internal problem ID [17422]
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 2.7 (Substitution Methods). Problems at page 108
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 10:06:44 AM
CAS classification : [_separable]

\begin{align*} \left (y^{4}+1\right ) y^{\prime }&=x^{4}+1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve((y(x)^4+1)*diff(y(x),x)=x^4+1,y(x), singsol=all)
 

\[ \frac {x^{5}}{5}+x -\frac {y^{5}}{5}-y+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 4.516 (sec). Leaf size: 141

DSolve[(y[x]^4+1)*D[y[x],x]==x^4+1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}-x^5-5 x-5 c_1\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}-x^5-5 x-5 c_1\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}-x^5-5 x-5 c_1\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}-x^5-5 x-5 c_1\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}-x^5-5 x-5 c_1\&,5\right ] \\ \end{align*}