67.2.55 problem Problem 20(b)

Internal problem ID [13941]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 20(b)
Date solved : Monday, March 31, 2025 at 08:19:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime }&=\left (25-6 x \right ) y \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 128

ode:=(x^2+2*x)*diff(diff(y(x),x),x)+(x^2+x+10)*diff(y(x),x) = (25-6*x)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-88447 x^{4} c_2 \,{\mathrm e}^{-x -2} \left (x +2\right )^{7} \operatorname {Ei}_{1}\left (-x -2\right )+11970 x^{4} c_2 \,{\mathrm e}^{-x} \left (x +2\right )^{7} \operatorname {Ei}_{1}\left (-x \right )+c_1 \,{\mathrm e}^{-x} \left (x +2\right )^{7} x^{4}-76477 c_2 \,x^{10}-970261 c_2 \,x^{9}-5171184 c_2 \,x^{8}-14871174 c_2 \,x^{7}-24496796 c_2 \,x^{6}-22249488 c_2 \,x^{5}-9184784 c_2 \,x^{4}-488880 c_2 \,x^{3}+131040 c_2 \,x^{2}-60480 c_2 x +40320 c_2}{x^{4}} \]

✓ Mathematica. Time used: 0.318 (sec). Leaf size: 114

ode=(2*x+x^2)*D[y[x],{x,2}]+ (10+x+x^2)*D[y[x],x]==(25-6*x)*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {4}{K[1]+2}-\frac {1}{2}+\frac {5}{2 K[1]}\right )dK[1]-\frac {1}{2} \int _1^x\left (-\frac {6}{K[2]+2}+1+\frac {5}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {-K[1]^2+11 K[1]+10}{2 K[1]^2+4 K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((6*x - 25)*y(x) + (x**2 + 2*x)*Derivative(y(x), (x, 2)) + (x**2 + x + 10)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False