29.2.27 problem 52

Internal problem ID [4660]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 52
Date solved : Sunday, March 30, 2025 at 03:33:09 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

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

\[ y = -\frac {4 x}{9}-\frac {1}{9}-\frac {2 \tan \left (-6 x +6 c_1 \right )}{27} \]

✓ Mathematica. Time used: 0.173 (sec). Leaf size: 49

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

\begin{align*} y(x)\to \frac {1}{81} \left (-36 x+\frac {1}{c_1 e^{12 i x}-\frac {i}{12}}-(9+6 i)\right ) \\ y(x)\to \frac {1}{27} (-12 x-(3+2 i)) \\ \end{align*}

✓ Sympy. Time used: 0.398 (sec). Leaf size: 48

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

\[ y{\left (x \right )} = \frac {- 12 C_{1} x + C_{1} \left (-3 + 2 i\right ) + 12 x e^{12 i x} + \left (3 + 2 i\right ) e^{12 i x}}{27 \left (C_{1} - e^{12 i x}\right )} \]