Internal problem ID [5314]
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]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2} x^{2}+4 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 28
dsolve(diff(y(x),x)=x^2*y(x)^2-4*x^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 \left ({\mathrm e}^{\frac {4 x^{3}}{3}} c_{1}+1\right )}{-1+{\mathrm e}^{\frac {4 x^{3}}{3}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.389 (sec). Leaf size: 30
DSolve[y'[x]==x^2*y[x]^2-4*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \tanh \left (\frac {2}{3} \left (x^3+3 c_1\right )\right ) \\ y(x)\to -2 \\ y(x)\to 2 \\ \end{align*}