Internal problem ID [10595]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page
37
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
\[ \boxed {y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.218 (sec). Leaf size: 39
dsolve((y(x)+x*(x^2+y(x)^2)^2)+(y(x)*(x^2+y(x)^2)^2-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\tan \left (\operatorname {RootOf}\left (-\tan \left (\textit {\_Z} \right )^{4} x^{4}-2 \tan \left (\textit {\_Z} \right )^{2} x^{4}-x^{4}+4 c_{1} -4 \textit {\_Z} \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 40
DSolve[(y[x]+x*(x^2+y[x]^2)^2)+(y[x]*(x^2+y[x]^2)^2-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\arctan \left (\frac {x}{y(x)}\right )+\frac {x^4}{4}+\frac {1}{2} x^2 y(x)^2+\frac {y(x)^4}{4}=c_1,y(x)\right ] \]