4.4 problem 1452

Internal problem ID [9031]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1452.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 y^{\prime }-4 y=0} \end {gather*}

Solution by Maple

Time used: 0.0 (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)
 

\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {15}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {15}\, x}{2}\right ) \]

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 49

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

\begin{align*} y(x)\to c_3 e^x+e^{-x/2} \left (c_2 \cos \left (\frac {\sqrt {15} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {15} x}{2}\right )\right ) \\ \end{align*}