28.1.19 problem 19

Internal problem ID [4325]
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
Date solved : Monday, January 27, 2025 at 09:02:45 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (1+x \right )^{2}+\left (4 y+1\right )^{2}+8 y x +1 \end{align*}

✓ Solution by Maple

Time used: 0.008 (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)
 

\[ y \left (x \right ) = -\frac {x}{4}-\frac {1}{4}-\frac {3 \tan \left (-6 x +6 c_{1} \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.185 (sec). Leaf size: 49

DSolve[D[y[x],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*}