63.1.116 problem 167

Internal problem ID [15556]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 167
Date solved : Thursday, October 02, 2025 at 10:19:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-7*diff(y(x),x)+6*y(x) = sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_2 +{\mathrm e}^{6 x} c_1 +\frac {7 \cos \left (x \right )}{74}+\frac {5 \sin \left (x \right )}{74} \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 66

ode=D[y[x],{x,2}]-7*D[y[x],x]+6*y[x]==Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^x \left (\int _1^x-\frac {1}{5} e^{-K[1]} \sin (K[1])dK[1]+e^{5 x} \int _1^x\frac {1}{5} e^{-6 K[2]} \sin (K[2])dK[2]+c_2 e^{5 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - sin(x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{6 x} + \frac {5 \sin {\left (x \right )}}{74} + \frac {7 \cos {\left (x \right )}}{74} \]