20.5.10 problem Problem 10

Internal problem ID [3693]
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
Date solved : Monday, January 27, 2025 at 07:55:27 AM
CAS classification : [_exact, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 46

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 \left (x \right ) &= {\mathrm e}^{-2 x} \sqrt {{\mathrm e}^{2 x} \left (-x^{3}+c_{1} \right )} \\ y \left (x \right ) &= -{\mathrm e}^{-2 x} \sqrt {{\mathrm e}^{2 x} \left (-x^{3}+c_{1} \right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 7.876 (sec). Leaf size: 47

DSolve[(2*y[x]^2*Exp[2*x]+3*x^2)+2*y[x]*Exp[2*x]*D[y[x],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*}