Internal problem ID [2213]
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 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _Bernoulli]
Solve \begin {gather*} \boxed {2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve((2*y(x)^2*exp(2*x)+3*x^2)+2*y(x)*exp(2*x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\mathrm e}^{-2 x} \sqrt {{\mathrm e}^{2 x} \left (-x^{3}+c_{1}\right )} \\ y \relax (x ) = -{\mathrm e}^{-2 x} \sqrt {{\mathrm e}^{2 x} \left (-x^{3}+c_{1}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.707 (sec). Leaf size: 47
DSolve[(2*y[x]^2*Exp[2*x]+3*x^2)+2*y[x]*Exp[2*x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {e^{-2 x} \left (-x^3+c_1\right )} \\ y(x)\to \sqrt {e^{-2 x} \left (-x^3+c_1\right )} \\ \end{align*}