60.4.16 problem 1464

Internal problem ID [11467]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1464
Date solved : Monday, January 27, 2025 at 11:22:26 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-3*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-2 x}+{\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +c_3 \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 34

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

\[ y(x)\to e^{-2 x} \left (c_2 e^{4 x} \cos (x)+c_1 e^{4 x} \sin (x)+c_3\right ) \]