38.2.49 problem 49

Internal problem ID [6478]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 49
Date solved : Monday, January 27, 2025 at 02:07:21 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

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

\[ y = \frac {1}{\left (-x +c_1 \right ) x} \]

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 23

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

\begin{align*} y(x)\to -\frac {1}{x^2-c_1 x} \\ y(x)\to 0 \\ \end{align*}