60.4.4 problem 1452

Internal problem ID [11455]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1452
Date solved : Monday, January 27, 2025 at 11:22:21 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 35

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

\[ y = {\mathrm e}^{x} c_{1} +{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {15}\, x}{2}\right ) c_{2} +c_3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {15}\, x}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 52

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

\[ y(x)\to e^{-x/2} \left (c_3 e^{3 x/2}+c_2 \cos \left (\frac {\sqrt {15} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {15} x}{2}\right )\right ) \]