83.30.12 problem 12

Internal problem ID [19320]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 12
Date solved : Monday, March 31, 2025 at 07:06:48 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=x*diff(diff(y(x),x),x)+diff(y(x),x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}}{4}+c_1 \ln \left (x \right )+c_2 \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 20

ode=x*D[y[x],{x,2}]+D[y[x],x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^2}{4}+c_1 \log (x)+c_2 \]

✓ Sympy. Time used: 0.171 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} + C_{2} \log {\left (x \right )} + \frac {x^{2}}{4} \]