83.8.5 problem 5

Internal problem ID [19052]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 5
Date solved : Thursday, March 13, 2025 at 01:34:10 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 19

ode:=diff(y(x),x) = (4*x+y(x)+1)^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.166 (sec). Leaf size: 41

ode=D[y[x],x]==(4*x+y[x]+1)^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}}-(1+2 i) \\ y(x)\to -4 x-(1+2 i) \\ \end{align*}

✓ Sympy. Time used: 0.364 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(4*x + y(x) + 1)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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