29.19.26 problem 539

Internal problem ID [5135]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 539
Date solved : Monday, January 27, 2025 at 10:13:49 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} 2 x y y^{\prime }+1-2 x^{3}-y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(2*x*y(x)*diff(y(x),x)+1-2*x^3-y(x)^2 = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.316 (sec). Leaf size: 37

DSolve[2 x y[x] D[y[x],x]+1-2 x^3-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {x^3+c_1 x+1} \\ y(x)\to \sqrt {x^3+c_1 x+1} \\ \end{align*}