28.1.34 problem 34

Internal problem ID [4340]
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 : 34
Date solved : Monday, January 27, 2025 at 09:06:09 AM
CAS classification : [_rational]

\begin{align*} 3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 22

dsolve(3*(x^2+y(x)^2)+x*(x^2+3*y(x)^2+6*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ c_{1} +\frac {{\mathrm e}^{y \left (x \right )} x^{3}}{3}+{\mathrm e}^{y \left (x \right )} y \left (x \right )^{2} x = 0 \]

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 26

DSolve[3*(x^2+y[x]^2)+x*(x^2+3*y[x]^2+6*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x^3 e^{y(x)}+3 x e^{y(x)} y(x)^2=c_1,y(x)\right ] \]