Internal problem ID [95]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\left (4 x +y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(diff(y(x),x) = (4*x+y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = -4 x -2 \tan \left (-2 x +2 c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 41
DSolve[y'[x] == (4*x+y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -4 x+\frac {1}{c_1 e^{4 i x}-\frac {i}{4}}-2 i \\ y(x)\to -4 x-2 i \\ \end{align*}