15.6.21 problem 21

Internal problem ID [2978]
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 : 21
Date solved : Monday, January 27, 2025 at 07:05:18 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.184 (sec). Leaf size: 34

dsolve([(y(x)+y(x)^3)+4*(x*y(x)^2-1)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-x \,{\mathrm e}^{4 \textit {\_Z}}-2 x \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{2 \textit {\_Z}}+4 \textit {\_Z} -x -2\right )} \]

✓ Solution by Mathematica

Time used: 0.227 (sec). Leaf size: 37

DSolve[{(y[x]+y[x]^3)+4*(x*y[x]^2-1)*D[y[x],x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=\frac {2 y(x)^2+4 \log (y(x))}{\left (y(x)^2+1\right )^2}-\frac {2}{\left (y(x)^2+1\right )^2},y(x)\right ] \]