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: 0.015 (sec). Leaf size: 35
dsolve(x=diff(y(x),x)^2+diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {x}{2}-\frac {\left (1+4 x \right )^{\frac {3}{2}}}{12}+c_{1} y \left (x \right ) = -\frac {x}{2}+\frac {\left (1+4 x \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*}