8.6.8 problem 8

Internal problem ID [778]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 8
Date solved : Monday, January 27, 2025 at 03:04:47 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

\[ y = \frac {3 x}{3 c_1 \,x^{3}+1} \]

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 24

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

\begin{align*} y(x)\to \frac {3 x}{1+3 c_1 x^3} \\ y(x)\to 0 \\ \end{align*}