Internal problem ID [4017]
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]
\[ \boxed {{y^{\prime }}^{2}+a y^{\prime }=-b} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 45
dsolve(diff(y(x),x)^2+a*diff(y(x),x)+b = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (-\frac {a}{2}-\frac {\sqrt {a^{2}-4 b}}{2}\right ) x +c_{1} y \left (x \right ) = \left (-\frac {a}{2}+\frac {\sqrt {a^{2}-4 b}}{2}\right ) x +c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 59
DSolve[(y'[x])^2+a y'[x]+b==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} x \sqrt {a^2-4 b}-\frac {a x}{2}+c_1 y(x)\to \frac {1}{2} x \sqrt {a^2-4 b}-\frac {a x}{2}+c_1 \end{align*}