63.1.89 problem 134

Internal problem ID [15529]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 134
Date solved : Thursday, October 02, 2025 at 10:19:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+10*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (c_1 \sin \left (3 x \right )+c_2 \cos \left (3 x \right )\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 26

ode=D[y[x],{x,2}]+2*D[y[x],x]+10*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} (c_2 \cos (3 x)+c_1 \sin (3 x)) \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*y(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (3 x \right )} + C_{2} \cos {\left (3 x \right )}\right ) e^{- x} \]