Internal problem ID [3687]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 433.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (1+y\right ) y^{\prime }-x^{2} \left (1-y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 30.295 (sec). Leaf size: 66
DSolve[(1+y[x])y'[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*}