52.1.36 problem 36

Internal problem ID [10407]
Book : Second order enumerated odes
Section : section 1
Problem number : 36
Date solved : Tuesday, September 30, 2025 at 07:23:11 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

\[ y = -{\mathrm e}^{-x} c_1 -\frac {\sin \left (x \right )}{2}-\frac {\cos \left (x \right )}{2}+c_2 \]

✓ Mathematica. Time used: 3.133 (sec). Leaf size: 41

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

\begin{align*} y(x)&\to \int _1^xe^{-K[2]} \left (c_1+\int _1^{K[2]}e^{K[1]} \sin (K[1])dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 19

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

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