59.1.505 problem 521

Internal problem ID [9677]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 521
Date solved : Monday, January 27, 2025 at 06:12:58 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {3 x}{2}} \left (c_{1} \sin \left (\frac {\sqrt {7}\, x}{2}\right )+c_{2} \cos \left (\frac {\sqrt {7}\, x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 42

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

\[ y(x)\to e^{-3 x/2} \left (c_2 \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {7} x}{2}\right )\right ) \]