15.19.2 problem 2

Internal problem ID [3286]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 2
Date solved : Monday, January 27, 2025 at 07:31:02 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: 0.006 (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: 0.073 (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*}