59.1.181 problem 183

Internal problem ID [9353]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 183
Date solved : Wednesday, March 05, 2025 at 07:47:57 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 26

ode:=4*x^2*(1+x)*diff(diff(y(x),x),x)+4*x*(4*x+1)*diff(y(x),x)-(49+27*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_{1} x^{7}+7 c_{2} x +6 c_{2}}{\left (x +1\right )^{2} x^{{7}/{2}}} \]

✓ Mathematica. Time used: 0.266 (sec). Leaf size: 102

ode=4*x^2*(1+x)*D[y[x],{x,2}]+4*x*(1+4*x)*D[y[x],x]-(49+27*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {4}{K[1]}-\frac {1}{2 (K[1]+1)}\right )dK[1]-\frac {1}{2} \int _1^x\left (\frac {3}{K[2]+1}+\frac {1}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {7 K[1]+8}{2 K[1]^2+2 K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*(x + 1)*Derivative(y(x), (x, 2)) + 4*x*(4*x + 1)*Derivative(y(x), x) - (27*x + 49)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False