29.23.23 problem 654

Internal problem ID [5245]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 654
Date solved : Monday, January 27, 2025 at 10:49:07 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (1-4 x +3 x y^{2}\right ) y^{\prime }&=\left (2-y^{2}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 60.200 (sec). Leaf size: 2348

DSolve[(1-4 x+3 x y[x]^2)D[y[x],x]==(2-y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
 

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