20.5.4 problem Problem 4

Internal problem ID [3687]
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
Date solved : Monday, January 27, 2025 at 07:55:23 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} 2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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: 0.260 (sec). Leaf size: 19

DSolve[2*x*Exp[y[x]]+(3*y[x]^2+x^2*Exp[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x^2 e^{y(x)}+y(x)^3=c_1,y(x)\right ] \]