Internal problem ID [2655]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\left (x +1\right )^{2}-\left (4 y+1\right )^{2}-8 y x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 19
dsolve(diff(y(x),x)=(x+1)^2+(4*y(x)+1)^2+8*x*y(x)+1,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{4}-\frac {1}{4}-\frac {3 \tan \left (-6 x +6 c_{1}\right )}{8} \]
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 49
DSolve[y'[x]==(x+1)^2+(4*y[x]+1)^2+8*x*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{16} \left (-4 x+\frac {1}{c_1 e^{12 i x}-\frac {i}{12}}-(4+6 i)\right ) \\ y(x)\to \frac {1}{8} (-2 x-(2+3 i)) \\ \end{align*}