29.27.6 problem 772

Internal problem ID [5356]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 772
Date solved : Monday, January 27, 2025 at 11:17:13 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}+2 y^{\prime }+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 45

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 47

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