29.15.25 problem 433

Internal problem ID [5031]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 433
Date solved : Monday, January 27, 2025 at 10:04:48 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

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

\[ y \left (x \right ) = 2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x^{3}}{6}-\frac {1}{2}}}{2}\right )+1 \]

✓ Solution by Mathematica

Time used: 22.285 (sec). Leaf size: 66

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

\begin{align*} y(x)\to 1+2 W\left (-\frac {1}{2} \sqrt {e^{-\frac {x^3}{3}-1+c_1}}\right ) \\ y(x)\to 1+2 W\left (\frac {1}{2} \sqrt {e^{-\frac {x^3}{3}-1+c_1}}\right ) \\ y(x)\to 1 \\ \end{align*}