Internal problem ID [3289]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 545.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y^{\prime } y x +x^{2} \left (a \,x^{3}+1\right )-6 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 45
dsolve(2*x*y(x)*diff(y(x),x)+x^2*(a*x^3+1) = 6*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {4 c_{1} x^{4}+4 a \,x^{3}+1}\, x}{2} \\ y \relax (x ) = \frac {\sqrt {4 c_{1} x^{4}+4 a \,x^{3}+1}\, x}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.558 (sec). Leaf size: 59
DSolve[2 x y[x] y'[x]+x^2(1+a x^3)==6 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \sqrt {4 a x^5+4 c_1 x^6+x^2} \\ y(x)\to \frac {1}{2} \sqrt {4 a x^5+4 c_1 x^6+x^2} \\ \end{align*}