Internal problem ID [3615]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 887.
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}+4 y y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.104 (sec). Leaf size: 126
dsolve(4*x*diff(y(x),x)^2+4*y(x)*diff(y(x),x) = 1,y(x), singsol=all)
\begin{align*} -\frac {c_{1} \left (\frac {-y \relax (x )+\sqrt {x +y \relax (x )^{2}}}{x}\right )^{\frac {3}{2}} x^{2}}{\left (-y \relax (x )+\sqrt {x +y \relax (x )^{2}}\right )^{2}}+x -\frac {x^{2}}{3 \left (-y \relax (x )+\sqrt {x +y \relax (x )^{2}}\right )^{2}} = 0 \\ \frac {\left (\frac {-2 y \relax (x )-2 \sqrt {x +y \relax (x )^{2}}}{x}\right )^{\frac {3}{2}} x^{2} c_{1}}{\left (y \relax (x )+\sqrt {x +y \relax (x )^{2}}\right )^{2}}+x -\frac {x^{2}}{3 \left (y \relax (x )+\sqrt {x +y \relax (x )^{2}}\right )^{2}} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.19 (sec). Leaf size: 4057
DSolve[4 x (y'[x])^2+4 y[x] y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
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