20.4.38 problem Problem 55

Internal problem ID [3673]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 55
Date solved : Monday, January 27, 2025 at 07:53:58 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 19

dsolve(diff(y(x),x)=(4*x+y(x)+2)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -4 x -2-2 \tan \left (-2 x +2 c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.172 (sec). Leaf size: 41

DSolve[D[y[x],x]==(4*x+y[x]+2)^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+2 i) \\ y(x)\to -4 x-(2+2 i) \\ \end{align*}