Internal problem ID [3504]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 772.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+2 y^{\prime }+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 35
dsolve(diff(y(x),x)^2+2*diff(y(x),x)+x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x +\frac {2 \left (1-x \right )^{\frac {3}{2}}}{3}+c_{1} \\ y \relax (x ) = -x -\frac {2 \left (1-x \right )^{\frac {3}{2}}}{3}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 47
DSolve[(y'[x])^2+2 y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{3} (1-x)^{3/2}-x+c_1 \\ y(x)\to \frac {2}{3} (1-x)^{3/2}-x+c_1 \\ \end{align*}