Internal problem ID [3584]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 853.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G], _dAlembert]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}+y y^{\prime }+a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 146
dsolve(x*diff(y(x),x)^2+y(x)*diff(y(x),x)+a = 0,y(x), singsol=all)
\begin{align*} -\frac {c_{1} \left (\frac {-y \relax (x )+\sqrt {-4 a x +y \relax (x )^{2}}}{x}\right )^{\frac {3}{2}} x^{2}}{\left (-y \relax (x )+\sqrt {-4 a x +y \relax (x )^{2}}\right )^{2}}+x +\frac {4 a \,x^{2}}{3 \left (-y \relax (x )+\sqrt {-4 a x +y \relax (x )^{2}}\right )^{2}} = 0 \\ \frac {\left (\frac {-2 y \relax (x )-2 \sqrt {-4 a x +y \relax (x )^{2}}}{x}\right )^{\frac {3}{2}} x^{2} c_{1}}{\left (y \relax (x )+\sqrt {-4 a x +y \relax (x )^{2}}\right )^{2}}+x +\frac {4 a \,x^{2}}{3 \left (y \relax (x )+\sqrt {-4 a x +y \relax (x )^{2}}\right )^{2}} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.298 (sec). Leaf size: 4845
DSolve[x (y'[x])^2+y[x] y'[x]+a==0,y[x],x,IncludeSingularSolutions -> True]
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