Internal problem ID [3785]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1076.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (x +2 y\right ) \left (y^{\prime }\right )^{3}+3 \left (x +y\right ) \left (y^{\prime }\right )^{2}+\left (2 x +y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.051 (sec). Leaf size: 65
dsolve((x+2*y(x))*diff(y(x),x)^3+3*(x+y(x))*diff(y(x),x)^2+(2*x+y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1}-x \\ y \relax (x ) = \frac {-\frac {c_{1} x}{2}-\frac {\sqrt {-3 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \\ y \relax (x ) = \frac {-\frac {c_{1} x}{2}+\frac {\sqrt {-3 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \\ y \relax (x ) = c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 130
DSolve[(x+2 y[x])(y'[x])^3+3 (x+y[x]) (y'[x])^2+ (2 x+y[x]) y'[x] ==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-x-\sqrt {-3 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (-x+\sqrt {-3 x^2+4 e^{c_1}}\right ) \\ y(x)\to c_1 \\ y(x)\to -x+c_1 \\ y(x)\to \frac {1}{2} \left (-\sqrt {3} \sqrt {-x^2}-x\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {3} \sqrt {-x^2}-x\right ) \\ \end{align*}