89.7.3 problem 3

Internal problem ID [24434]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:31:29 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (9 x +4 y+1\right )^{2} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(y(x),x) = (9*x+4*y(x)+1)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {9 x}{4}-\frac {1}{4}-\frac {3 \tan \left (-6 x +6 c_1 \right )}{8} \]

✓ Mathematica. Time used: 0.1 (sec). Leaf size: 49

ode=D[y[x],x]==(9*x+4*y[x]+1)^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{16} \left (-36 x+\frac {1}{c_1 e^{12 i x}-\frac {i}{12}}-(4+6 i)\right )\\ y(x)&\to \frac {1}{8} (-18 x-(2+3 i)) \end{align*}

✓ Sympy. Time used: 0.244 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(9*x + 4*y(x) + 1)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {- 18 C_{1} x + C_{1} \left (-2 + 3 i\right ) + 18 x e^{12 i x} + \left (2 + 3 i\right ) e^{12 i x}}{8 \left (C_{1} - e^{12 i x}\right )} \]