29.32.26 problem 961

Internal problem ID [5538]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 32
Problem number : 961
Date solved : Monday, January 27, 2025 at 11:35:54 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 32

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

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

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 53

DSolve[x y[x] (D[y[x],x])^2+(x+y[x])D[y[x],x]+1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {2} \sqrt {-x+c_1} \\ y(x)\to \sqrt {2} \sqrt {-x+c_1} \\ y(x)\to -\log (x)+c_1 \\ \end{align*}