Internal problem ID [5280]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 25 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Riccati]
\[ \boxed {-y-3 x^{2} \left (x^{2}+y^{2}\right )+y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve((-y(x)-3*x^2*(x^2+y(x)^2))+x*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \tan \left (x^{3}+3 c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.184 (sec). Leaf size: 14
DSolve[(-y[x]-3*x^2*(x^2+y[x]^2))+x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \tan \left (x^3+c_1\right ) \]