75.15.5 problem 436

Internal problem ID [16956]
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 : 436
Date solved : Tuesday, January 28, 2025 at 09:43:42 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=0,y(0) = 6, D(y)(0) = 10],y(x), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{3 x}+4 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 17

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==0,{y[0]==6,Derivative[1][y][0] ==10}},y[x],x,IncludeSingularSolutions -> True]
 

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