Internal problem ID [3526]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 794.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\left (1+2 x \right ) y^{\prime }-x \left (1-x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 45
dsolve(diff(y(x),x)^2-(1+2*x)*diff(y(x),x)-x*(1-x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x}{2}+\frac {x^{2}}{2}-\frac {\left (8 x +1\right )^{\frac {3}{2}}}{24}+c_{1} \\ y \relax (x ) = \frac {x}{2}+\frac {x^{2}}{2}+\frac {\left (8 x +1\right )^{\frac {3}{2}}}{24}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 62
DSolve[(y'[x])^2-(1+2 x)y'[x]-x(1-x)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{2}+\frac {x}{2}-\frac {1}{24} (8 x+1)^{3/2}+c_1 \\ y(x)\to \frac {1}{2} \left (x^2+x+\frac {1}{12} (8 x+1)^{3/2}\right )+c_1 \\ \end{align*}