40.3.24 problem 25 (L)

Internal problem ID [6628]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (L)
Date solved : Monday, January 27, 2025 at 02:16:19 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

\[ y = \frac {x^{2}}{x^{3}+c_1} \]

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {x^2}{x^3+c_1} \\ y(x)\to 0 \\ \end{align*}