59.1.494 problem 510

Internal problem ID [9666]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 510
Date solved : Wednesday, March 05, 2025 at 07:57:06 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.067 (sec). Leaf size: 77

ode:=(2*x^2+x+1)*diff(diff(y(x),x),x)+(1+7*x)*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} \operatorname {hypergeom}\left (\left [\frac {1}{2}, 2\right ], \left [-\frac {\left (-7 \sqrt {7}+3 i\right ) \sqrt {7}}{28}\right ], \frac {1}{2}+\frac {i \left (-4 x -1\right ) \sqrt {7}}{14}\right )+c_{2} \left (i \sqrt {7}+4 x +1\right )^{-\frac {3}{4}+\frac {3 i \sqrt {7}}{28}} \left (i \sqrt {7}-4 x -1\right )^{-\frac {3}{4}-\frac {3 i \sqrt {7}}{28}} \left (x +1\right ) \]

✓ Mathematica. Time used: 0.943 (sec). Leaf size: 119

ode=(1+x+2*x^2)*D[y[x],{x,2}]+(1+7*x)*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((7*x + 1)*Derivative(y(x), x) + (2*x**2 + x + 1)*Derivative(y(x), (x, 2)) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False