84.30.1 problem 18.11

Internal problem ID [22290]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 18. Linear differential equations with variable coefficients. Supplementary problems
Problem number : 18.11
Date solved : Thursday, October 02, 2025 at 08:37:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y x&=0 \end{align*}

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 76

Order:=6; 
ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)+2*x*y(x) = 0; 
dsolve(ode,y(x),type='series',x=1);
 

\[ y = \left (1-\left (x -1\right )^{2}+\frac {2 \left (x -1\right )^{3}}{3}-\frac {\left (x -1\right )^{4}}{3}+\frac {7 \left (x -1\right )^{5}}{30}\right ) y \left (1\right )+\left (x -1-\frac {3 \left (x -1\right )^{2}}{2}+\frac {7 \left (x -1\right )^{3}}{6}-\frac {19 \left (x -1\right )^{4}}{24}+\frac {61 \left (x -1\right )^{5}}{120}\right ) y^{\prime }\left (1\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 85

ode=D[y[x],{x,2}]+3*D[y[x],x]+2*x*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,1,5}]
 

\[ y(x)\to c_1 \left (\frac {7}{30} (x-1)^5-\frac {1}{3} (x-1)^4+\frac {2}{3} (x-1)^3-(x-1)^2+1\right )+c_2 \left (\frac {61}{120} (x-1)^5-\frac {19}{24} (x-1)^4+\frac {7}{6} (x-1)^3-\frac {3}{2} (x-1)^2+x-1\right ) \]

✓ Sympy. Time used: 0.288 (sec). Leaf size: 60

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x) + 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_ordinary",x0=1,n=6)
 

\[ y{\left (x \right )} = C_{2} \left (x - \frac {19 \left (x - 1\right )^{4}}{24} + \frac {7 \left (x - 1\right )^{3}}{6} - \frac {3 \left (x - 1\right )^{2}}{2} - 1\right ) + C_{1} \left (- \frac {\left (x - 1\right )^{4}}{3} + \frac {2 \left (x - 1\right )^{3}}{3} - \left (x - 1\right )^{2} + 1\right ) + O\left (x^{6}\right ) \]