75.15.9 problem 440

Internal problem ID [16960]
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 : 440
Date solved : Tuesday, January 28, 2025 at 09:43:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(4*diff(y(x),x$2)-8*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_{1} \sin \left (\frac {x}{2}\right )+c_{2} \cos \left (\frac {x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 28

DSolve[4*D[y[x],{x,2}]-8*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (c_2 \cos \left (\frac {x}{2}\right )+c_1 \sin \left (\frac {x}{2}\right )\right ) \]