28.1.115 problem 138

Internal problem ID [4421]
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 : 138
Date solved : Monday, January 27, 2025 at 09:16:39 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

\begin{align*} 2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 38

dsolve(2*x^3*y(x)*diff(y(x),x)+3*x^2*y(x)^2+7=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\sqrt {c_{1} x -7 x^{2}}}{x^{2}} \\ y \left (x \right ) &= -\frac {\sqrt {c_{1} x -7 x^{2}}}{x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 42

DSolve[2*x^3*y[x]*D[y[x],x]+3*x^2*y[x]^2+7==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-7 x+c_1}}{x^{3/2}} \\ y(x)\to \frac {\sqrt {-7 x+c_1}}{x^{3/2}} \\ \end{align*}