Internal problem ID [7991]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 412.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _dAlembert]
\[ \boxed {x {y^{\prime }}^{2}+y y^{\prime }+a=0} \]
✓ Solution by Maple
Time used: 0.063 (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 \left (x \right )+\sqrt {-4 a x +y \left (x \right )^{2}}}{x}\right )}^{\frac {3}{2}} x^{2}}{\left (-y \left (x \right )+\sqrt {-4 a x +y \left (x \right )^{2}}\right )^{2}}+x +\frac {4 a \,x^{2}}{3 \left (-y \left (x \right )+\sqrt {-4 a x +y \left (x \right )^{2}}\right )^{2}} = 0 \\ \frac {{\left (\frac {-2 y \left (x \right )-2 \sqrt {-4 a x +y \left (x \right )^{2}}}{x}\right )}^{\frac {3}{2}} x^{2} c_{1}}{\left (y \left (x \right )+\sqrt {-4 a x +y \left (x \right )^{2}}\right )^{2}}+x +\frac {4 a \,x^{2}}{3 \left (y \left (x \right )+\sqrt {-4 a x +y \left (x \right )^{2}}\right )^{2}} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.303 (sec). Leaf size: 4845
DSolve[a + y[x]*y'[x] + x*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
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