Internal problem ID [150]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 31(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-3 x^{2} \left (7+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(diff(y(x),x) = 3*x^2*(7+y(x)),y(x), singsol=all)
\[ y \relax (x ) = -7+{\mathrm e}^{x^{3}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 20
DSolve[y'[x] == 3*x^2*(7+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -7+c_1 e^{x^3} \\ y(x)\to -7 \\ \end{align*}