8.5.17 problem 17

Internal problem ID [745]
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
Date solved : Tuesday, March 04, 2025 at 11:40:23 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.143 (sec). Leaf size: 41

ode=D[y[x],x] == (4*x+y[x])^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.307 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(4*x + y(x))**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2 \left (- 2 C_{1} x + i C_{1} + 2 x e^{4 i x} + i e^{4 i x}\right )}{C_{1} - e^{4 i x}} \]