38.1.12 problem 12

Internal problem ID [6429]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Test excercise 24. page 1067
Problem number : 12
Date solved : Monday, January 27, 2025 at 02:02:44 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {1}{x^{2} \left (c_1 x +1\right )} \]

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {1}{x^2+c_1 x^3} \\ y(x)\to 0 \\ \end{align*}