10.5.15 problem 19

Internal problem ID [1207]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 19
Date solved : Monday, January 27, 2025 at 04:45:13 AM
CAS classification : [_separable]

\begin{align*} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 37

dsolve(x^2*y(x)^3+x*(1+y(x)^2)*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x^{2}}{2}-c_1} \sqrt {\frac {{\mathrm e}^{x^{2}+2 c_1}}{\operatorname {LambertW}\left ({\mathrm e}^{x^{2}+2 c_1}\right )}} \]

✓ Solution by Mathematica

Time used: 3.664 (sec). Leaf size: 46

DSolve[x^2*y[x]^3+x*(1+y[x]^2)*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {W\left (e^{x^2-2 c_1}\right )}} \\ y(x)\to \frac {1}{\sqrt {W\left (e^{x^2-2 c_1}\right )}} \\ y(x)\to 0 \\ \end{align*}