76.13.12 problem 12

Internal problem ID [17594]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 10:44:48 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 22

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

\[ y(x)\to e^{-x} (c_2 \cos (x)+c_1 \sin (x)) \]