29.27.28 problem 794

Internal problem ID [5378]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 794
Date solved : Monday, January 27, 2025 at 11:17:32 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-\left (1+2 x \right ) y^{\prime }-x \left (1-x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 50

dsolve(diff(y(x),x)^2-(1+2*x)*diff(y(x),x)-x*(1-x) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\left (-8 x -1\right ) \sqrt {8 x +1}}{24}+\frac {x^{2}}{2}+\frac {x}{2}+c_{1} \\ y \left (x \right ) &= \frac {x}{2}+\frac {\left (8 x +1\right )^{{3}/{2}}}{24}+\frac {x^{2}}{2}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 62

DSolve[(D[y[x],x])^2-(1+2*x)*D[y[x],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*}