Internal problem ID [3901]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 654.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\left (1-4 x +3 y^{2} x \right ) y^{\prime }-\left (2-y^{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve((1-4*x+3*x*y(x)^2)*diff(y(x),x) = (2-y(x)^2)*y(x),y(x), singsol=all)
\[ x +\frac {1}{y \left (x \right )^{2}}-\frac {c_{1}}{y \left (x \right )^{2} \sqrt {y \left (x \right )^{2}-2}} = 0 \]
✓ Solution by Mathematica
Time used: 60.163 (sec). Leaf size: 2348
DSolve[(1-4 x+3 x y[x]^2)y'[x]==(2-y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
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