54.4.11 problem 1464

Internal problem ID [12733]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1464
Date solved : Wednesday, October 01, 2025 at 02:21:28 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to e^{-2 x} \left (c_2 e^{4 x} \cos (x)+c_1 e^{4 x} \sin (x)+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.134 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*y(x) - 3*Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{- 2 x} + \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{2 x} \]