28.1.105 problem 128

Internal problem ID [4411]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 128
Date solved : Monday, January 27, 2025 at 09:15:09 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 56

dsolve((exp(x)+3*y(x)^2)+(2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 2.058 (sec). Leaf size: 62

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

\begin{align*} y(x)\to -\frac {\sqrt {-e^x \left (x^2-2 x+2\right )+c_1}}{x^{3/2}} \\ y(x)\to \frac {\sqrt {-e^x \left (x^2-2 x+2\right )+c_1}}{x^{3/2}} \\ \end{align*}