Internal problem ID [13410]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.4 (e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _dAlembert]
\[ \boxed {4 y x^{3}+\left (x^{4}-y^{4}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 23
dsolve(4*x^3*y(x)+(x^4-y(x)^4)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-5 \textit {\_Z} \,c_{1}^{4} x^{4}+\textit {\_Z}^{5}-1\right )}{c_{1}} \]
✓ Solution by Mathematica
Time used: 1.472 (sec). Leaf size: 131
DSolve[4*x^3*y[x]+(x^4-y[x]^4)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,5\right ] \\ y(x)\to 0 \\ \end{align*}