Internal problem ID [6067]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
190
Problem number: 1(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x^{2} y^{2}=-4 x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve(diff(y(x),x)=x^2*y(x)^2-4*x^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 \left ({\mathrm e}^{\frac {4 x^{3}}{3}} c_{1} +1\right )}{-1+{\mathrm e}^{\frac {4 x^{3}}{3}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.258 (sec). Leaf size: 52
DSolve[y'[x]==x^2*y[x]^2-4*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2-2 e^{\frac {4 x^3}{3}+4 c_1}}{1+e^{\frac {4 x^3}{3}+4 c_1}} y(x)\to -2 y(x)\to 2 \end{align*}