Internal problem ID [2716]
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]`]]
\[ \boxed {2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ x^{2} {\mathrm e}^{y \left (x \right )}+y \left (x \right )^{3}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.258 (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]
\[ \text {Solve}\left [x^2 e^{y(x)}+y(x)^3=c_1,y(x)\right ] \]