77.1.3 problem 1 (c) (page 9)

Internal problem ID [17822]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 1 (c) (page 9)
Date solved : Monday, March 31, 2025 at 04:33:23 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = -\sin \left (x \right )+c_1 x +c_2 \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.068 (sec). Leaf size: 10

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

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