Internal problem ID [106]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]]]
Solve \begin {gather*} \boxed {{\mathrm e}^{y} x y^{\prime }-2 \,{\mathrm e}^{y}-2 \,{\mathrm e}^{2 x} x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 20
dsolve(exp(y(x))*x*diff(y(x),x) = 2*exp(y(x))+2*exp(2*x)*x^3,y(x), singsol=all)
\[ y \relax (x ) = \ln \left ({\mathrm e}^{2 x} x^{2}-c_{1} x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 1.036 (sec). Leaf size: 18
DSolve[Exp[y[x]]*x*y'[x] == 2*Exp[y[x]]+2*Exp[2*x]*x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (x^2 \left (e^{2 x}+c_1\right )\right ) \\ \end{align*}