Internal problem ID [4020]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 780.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}+x y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 63
dsolve(diff(y(x),x)^2+x*diff(y(x),x)+1 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {x^{2}}{4}-\frac {x \sqrt {x^{2}-4}}{4}+\ln \left (x +\sqrt {x^{2}-4}\right )+c_{1} y \left (x \right ) = \frac {x \sqrt {x^{2}-4}}{4}-\ln \left (x +\sqrt {x^{2}-4}\right )-\frac {x^{2}}{4}+c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 87
DSolve[(y'[x])^2+x y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{4}-\frac {1}{4} \sqrt {x^2-4} x-\log \left (\sqrt {x^2-4}-x\right )+c_1 y(x)\to -\frac {x^2}{4}+\frac {1}{4} \sqrt {x^2-4} x+\log \left (\sqrt {x^2-4}-x\right )+c_1 \end{align*}