56.3.1 problem 1

Internal problem ID [8859]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 1
Date solved : Monday, January 27, 2025 at 05:07:14 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+c y^{\prime }+k y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(diff(y(x),x$2)+c*diff(y(x),x)+k*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {\left (-c +\sqrt {c^{2}-4 k}\right ) x}{2}}+c_{2} {\mathrm e}^{-\frac {\left (c +\sqrt {c^{2}-4 k}\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 7.017 (sec). Leaf size: 2548

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

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