47.4.1 problem 49

Internal problem ID [7478]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number : 49
Date solved : Monday, January 27, 2025 at 03:01:47 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 34

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

\[ y(x)\to e^{-\left (\left (1+\sqrt {2}\right ) x\right )} \left (c_2 e^{2 \sqrt {2} x}+c_1\right ) \]