Internal problem ID [3509]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 777.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+a y^{\prime }+b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.085 (sec). Leaf size: 45
dsolve(diff(y(x),x)^2+a*diff(y(x),x)+b = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-\frac {a}{2}-\frac {\sqrt {a^{2}-4 b}}{2}\right ) x +c_{1} \\ y \relax (x ) = \left (-\frac {a}{2}+\frac {\sqrt {a^{2}-4 b}}{2}\right ) x +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 53
DSolve[(y'[x])^2+a y'[x]+b==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} x \left (\sqrt {a^2-4 b}+a\right )+c_1 \\ y(x)\to \frac {1}{2} x \left (\sqrt {a^2-4 b}-a\right )+c_1 \\ \end{align*}