50.3.14 problem 14

Internal problem ID [10158]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 07:05:23 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }+y&=x \end{align*}

With initial conditions

\begin{align*} y^{\prime }\left (0\right )&=0 \\ y \left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.552 (sec). Leaf size: 447

ode:=diff(diff(diff(y(x),x),x),x)+diff(y(x),x)+y(x) = x; 
ic:=[D(y)(0) = 0, y(0) = 0, (D@@2)(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 1546

ode=D[y[x],{x,3}]+D[y[x],x]+y[x]==x; 
ic={Derivative[1][y][1] == 0,y[0]==0,Derivative[2][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {Subs(Derivative(y(x), x), x, 0): 0, y(0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out