Internal problem ID [4578]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x y^{\prime }+3 y-y^{2} x^{2}=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = \frac {1}{x^{2} \left (c_{1} x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 22
DSolve[x*y'[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*}