Internal problem ID [12147]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y^{\prime } \left (x^{2} y^{3}+x y\right )=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 70
dsolve(diff(y(x),x)*(x^2*y(x)^3+x*y(x))=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {x \left (2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {2 x -1}{2 x}}}{2}\right ) x +2 x -1\right )}}{x} y \left (x \right ) = -\frac {\sqrt {x \left (2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {2 x -1}{2 x}}}{2}\right ) x +2 x -1\right )}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 76
DSolve[y'[x]*(x^2*y[x]^3+x*y[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*}