15.6.15 problem 15

Internal problem ID [2972]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 15
Date solved : Monday, January 27, 2025 at 07:04:59 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 2 y&=\left (y^{4}+x \right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(2*y(x)=(y(x)^4+x)*diff(y(x),x),y(x), singsol=all)
 

\[ x -\frac {y^{4}}{7}-\sqrt {y}\, c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 60.129 (sec). Leaf size: 257

DSolve[2*y[x]==(y[x]^4+x)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,5\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,6\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,7\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,8\right ] \\ \end{align*}