7.5.17 problem 17

Internal problem ID [121]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 17
Date solved : Friday, February 07, 2025 at 07:52:57 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

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

\[ y = -4 x -2 \tan \left (-2 x +2 c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.139 (sec). Leaf size: 41

DSolve[D[y[x],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*}