Internal problem ID [4123]
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]
\[ \boxed {4 x {y^{\prime }}^{2}+4 y y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.032 (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 \left (x \right )+\sqrt {x +y \left (x \right )^{2}}}{x}\right )}^{\frac {3}{2}} x^{2}}{\left (-y \left (x \right )+\sqrt {x +y \left (x \right )^{2}}\right )^{2}}+x -\frac {x^{2}}{3 \left (-y \left (x \right )+\sqrt {x +y \left (x \right )^{2}}\right )^{2}} = 0 \frac {{\left (\frac {-2 y \left (x \right )-2 \sqrt {x +y \left (x \right )^{2}}}{x}\right )}^{\frac {3}{2}} x^{2} c_{1}}{\left (y \left (x \right )+\sqrt {x +y \left (x \right )^{2}}\right )^{2}}+x -\frac {x^{2}}{3 \left (y \left (x \right )+\sqrt {x +y \left (x \right )^{2}}\right )^{2}} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 60.239 (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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