Internal problem ID [558]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
dsolve(y(x)+(2*x-exp(y(x))*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\[ \frac {\left (-y \left (x \right )^{2}+2 y \left (x \right )-2\right ) {\mathrm e}^{y \left (x \right )}+x y \left (x \right )^{2}-c_{1}}{y \left (x \right )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 32
DSolve[y[x]+(2*x-Exp[y[x]]*y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {e^{y(x)} \left (y(x)^2-2 y(x)+2\right )}{y(x)^2}+\frac {c_1}{y(x)^2},y(x)\right ] \]