Internal problem ID [2685]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 50.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {y \left (y^{2}+1\right )+x \left (y^{2}-x +1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 153
dsolve((y(x)*(y(x)^2+1))+( x*(y(x)^2-x+1))*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1}+\frac {-\arctanh \left (\frac {\sqrt {-\frac {2 x^{2}}{\left (x -1\right )^{2} \left (\frac {1}{y \relax (x )^{2}}-\frac {1}{x -1}\right )}}\, \left (x -1\right )}{x \sqrt {\frac {\frac {2}{\frac {1}{y \relax (x )^{2}}-\frac {1}{x -1}}+2 x -2}{x -1}}}\right ) \sqrt {-\frac {2 x^{2}}{\left (x -1\right )^{2} \left (\frac {1}{y \relax (x )^{2}}-\frac {1}{x -1}\right )}}+\sqrt {\frac {\frac {2}{\frac {1}{y \relax (x )^{2}}-\frac {1}{x -1}}+2 x -2}{x -1}}}{\sqrt {-\frac {2 x^{2}}{\left (x -1\right )^{2} \left (\frac {1}{y \relax (x )^{2}}-\frac {1}{x -1}\right )}}} = 0 \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 34
DSolve[(y[x]*(y[x]^2+1))+( x*(y[x]^2-x+1))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \left (-\text {ArcTan}(y(x))-\frac {1}{y(x)}\right )+\frac {1}{2 x y(x)}=c_1,y(x)\right ] \]