75.15.12 problem 443

Internal problem ID [16963]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 443
Date solved : Tuesday, January 28, 2025 at 09:43:49 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 9

dsolve([diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 11

DSolve[{D[y[x],{x,2}]-2*D[y[x],x]+2*y[x]==0,{y[0]==0,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \sin (x) \]