75.15.13 problem 444

Internal problem ID [16964]
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 : 444
Date solved : Tuesday, January 28, 2025 at 09:43:51 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 24

dsolve([diff(y(x),x$2)-2*diff(y(x),x)+3*y(x)=0,y(0) = 1, D(y)(0) = 3],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (\sqrt {2}\, \sin \left (\sqrt {2}\, x \right )+\cos \left (\sqrt {2}\, x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 32

DSolve[{D[y[x],{x,2}]-2*D[y[x],x]+3*y[x]==0,{y[0]==1,Derivative[1][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (\sqrt {2} \sin \left (\sqrt {2} x\right )+\cos \left (\sqrt {2} x\right )\right ) \]