Internal problem ID [2079]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 50.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {3 y x +\left (3 x^{2}+y^{2}\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 4.016 (sec). Leaf size: 21
dsolve([(3*x*y(x))+(3*x^2+y(x)^2)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {-3 x^{2}+\sqrt {9 x^{4}+1}} \]
✓ Solution by Mathematica
Time used: 8.701 (sec). Leaf size: 26
DSolve[{(3*x*y[x])+(3*x^2+y[x]^2)*y'[x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {\sqrt {9 x^4+1}-3 x^2} \]