Internal problem ID [2338]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 38, page 173
Problem number: 1.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {-{y^{\prime }}^{2}-y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 40
dsolve(x=diff(y(x),x)^2+diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (-4 x -1\right ) \sqrt {4 x +1}}{12}-\frac {x}{2}+c_{1} \\ y \left (x \right ) &= -\frac {x}{2}+\frac {\left (4 x +1\right )^{\frac {3}{2}}}{12}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 54
DSolve[x==y'[x]^2+y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-\frac {1}{6} (4 x+1)^{3/2}-x\right )+c_1 \\ y(x)\to \frac {1}{12} \left ((4 x+1)^{3/2}-6 x+12 c_1\right ) \\ \end{align*}