83.40.1 problem 1

Internal problem ID [19394]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (E) at page 140
Problem number : 1
Date solved : Thursday, March 13, 2025 at 02:23:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +x \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 17

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

\[ y(x)\to x+c_1 \cos (x)+c_2 \sin (x) \]

✓ Sympy. Time used: 0.063 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )} + x \]