51.4.12 problem 12

Internal problem ID [10369]
Book : First order enumerated odes
Section : section 4. First order odes solved using series method
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 07:22:40 PM
CAS classification : [_linear]

\begin{align*} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x +\sin \left (x \right ) \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 32

Order:=6; 
ode:=cos(x)*diff(y(x),x)+y(x)/x = x+sin(x); 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \frac {c_1 \left (1-\frac {1}{4} x^{2}-\frac {1}{48} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x}+x^{2} \left (\frac {2}{3}+\frac {1}{10} x^{2}+\operatorname {O}\left (x^{4}\right )\right ) \]

✗ Mathematica

ode=Cos[x]*D[y[x],x]+y[x]/x==x+Sin[x]; 
AsymptoticDSolveValue[ode,y[x],{x,0,5}]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - sin(x) + cos(x)*Derivative(y(x), x) + y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

ValueError : ODE -x - sin(x) + cos(x)*Derivative(y(x), x) + y(x)/x does not match hint 1st_power_series