8.5.28 problem 28

Internal problem ID [756]
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
Date solved : Monday, January 27, 2025 at 03:03:20 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} {\mathrm e}^{y} x y^{\prime }&=2 \,{\mathrm e}^{y}+2 \,{\mathrm e}^{2 x} x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve(exp(y(x))*x*diff(y(x),x) = 2*exp(y(x))+2*exp(2*x)*x^3,y(x), singsol=all)
 

\[ y = \ln \left (x^{2} \left ({\mathrm e}^{2 x}-c_1 \right )\right ) \]

✓ Solution by Mathematica

Time used: 4.266 (sec). Leaf size: 18

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

\[ y(x)\to \log \left (x^2 \left (e^{2 x}+c_1\right )\right ) \]