Internal problem ID [4411]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 6.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {-a y^{\prime }-b {y^{\prime }}^{2}=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 80
dsolve(x=a*diff(y(x),x)+b*(diff(y(x),x))^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (a^{2}+4 x b \right )^{\frac {3}{2}}+12 c_{1} b^{2}-6 a x b}{12 b^{2}} \\ y \left (x \right ) &= \frac {12 c_{1} b^{2}-a^{2} \sqrt {a^{2}+4 x b}-6 a x b -4 b x \sqrt {a^{2}+4 x b}}{12 b^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 74
DSolve[x==a*y'[x]+b*(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (a^2+4 b x\right )^{3/2}-6 a b x+12 b^2 c_1}{12 b^2} \\ y(x)\to -\frac {\frac {\left (a^2+4 b x\right )^{3/2}}{6 b}+a x}{2 b}+c_1 \\ \end{align*}