Internal problem ID [2207]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page
91
Problem number: Problem 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {2 \,{\mathrm e}^{y} x +\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 16
dsolve(2*x*exp(y(x))+(3*y(x)^2+x^2*exp(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ x^{2} {\mathrm e}^{y \relax (x )}+y \relax (x )^{3}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.255 (sec). Leaf size: 19
DSolve[2*x*Exp[y[x]]+(3*y[x]^2+x^2*Exp[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2 e^{y(x)}+y(x)^3=c_1,y(x)\right ] \]