Internal problem ID [3614]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 886.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _dAlembert]
Solve \begin {gather*} \boxed {4 x \left (y^{\prime }\right )^{2}-3 y y^{\prime }+3=0} \end {gather*}
✓ Solution by Maple
Time used: 0.09 (sec). Leaf size: 153
dsolve(4*x*diff(y(x),x)^2-3*y(x)*diff(y(x),x)+3 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2 \sqrt {x \left (3+\sqrt {16 c_{1} x +9}\right )}}{3}-\frac {2 x}{\sqrt {x \left (3+\sqrt {16 c_{1} x +9}\right )}} \\ y \relax (x ) = \frac {2 \sqrt {x \left (3+\sqrt {16 c_{1} x +9}\right )}}{3}+\frac {2 x}{\sqrt {x \left (3+\sqrt {16 c_{1} x +9}\right )}} \\ y \relax (x ) = -\frac {2 \sqrt {-x \left (-3+\sqrt {16 c_{1} x +9}\right )}}{3}-\frac {2 x}{\sqrt {-x \left (-3+\sqrt {16 c_{1} x +9}\right )}} \\ y \relax (x ) = \frac {2 \sqrt {-x \left (-3+\sqrt {16 c_{1} x +9}\right )}}{3}+\frac {2 x}{\sqrt {-x \left (-3+\sqrt {16 c_{1} x +9}\right )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.639 (sec). Leaf size: 187
DSolve[4 x (y'[x])^2-3 y[x] y'[x]+3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {432 x-e^{-\frac {c_1}{2}} \left (-144 x+e^{c_1}\right ){}^{3/2}+e^{c_1}}}{6 \sqrt {3}} \\ y(x)\to \frac {\sqrt {432 x-e^{-\frac {c_1}{2}} \left (-144 x+e^{c_1}\right ){}^{3/2}+e^{c_1}}}{6 \sqrt {3}} \\ y(x)\to -\frac {\sqrt {432 x+e^{-\frac {c_1}{2}} \left (-144 x+e^{c_1}\right ){}^{3/2}+e^{c_1}}}{6 \sqrt {3}} \\ y(x)\to \frac {\sqrt {432 x+e^{-\frac {c_1}{2}} \left (-144 x+e^{c_1}\right ){}^{3/2}+e^{c_1}}}{6 \sqrt {3}} \\ \end{align*}