Internal problem ID [15234]
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 ODE’s). Section 15.2 Homogeneous differential equations with
constant coefficients. Exercises page 121
Problem number: 444.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+3 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (\sqrt {2}\, \sin \left (\sqrt {2}\, x \right )+\cos \left (\sqrt {2}\, x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 32
DSolve[{y''[x]-2*y'[x]+3*y[x]==0,{y[0]==1,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (\sqrt {2} \sin \left (\sqrt {2} x\right )+\cos \left (\sqrt {2} x\right )\right ) \]