82.12.23 problem Ex. 25

Internal problem ID [18788]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 25
Date solved : Tuesday, January 28, 2025 at 12:17:26 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

Solution by Maple

Time used: 0.013 (sec). Leaf size: 78

dsolve((x^2*y(x)^3+x*y(x))*diff(y(x),x)=1,y(x), singsol=all)
 
\begin{align*} y \left (x \right ) &= \frac {\sqrt {2 x^{2} \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {2 x -1}{2 x}}}{2}\right )+2 x^{2}-x}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {2 x^{2} \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {2 x -1}{2 x}}}{2}\right )+2 x^{2}-x}}{x} \\ \end{align*}

Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 76

DSolve[(x^2*y[x]^3+x*y[x])*D[y[x],x]==1,y[x],x,IncludeSingularSolutions -> True]
 
\begin{align*} y(x)\to -\frac {\sqrt {2 x W\left (c_1 e^{\frac {1}{2 x}-1}\right )+2 x-1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {2 x W\left (c_1 e^{\frac {1}{2 x}-1}\right )+2 x-1}}{\sqrt {x}} \\ \end{align*}