60.4.14 problem 1467

Internal problem ID [11437]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1467
Date solved : Sunday, March 30, 2025 at 08:22:13 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 380

ode:=diff(diff(diff(y(x),x),x),x)+a2*diff(diff(y(x),x),x)+a1*diff(y(x),x)+a0*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 84

ode=a0*y[x] + a1*D[y[x],x] + a2*D[y[x],{x,2}] + Derivative[3][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,1\right ]}+c_2 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,2\right ]}+c_3 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,3\right ]} \]

✓ Sympy. Time used: 1.651 (sec). Leaf size: 653

from sympy import * 
x = symbols("x") 
a0 = symbols("a0") 
a1 = symbols("a1") 
a2 = symbols("a2") 
y = Function("y") 
ode = Eq(a0*y(x) + a1*Derivative(y(x), x) + a2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]