40.14.4 problem 25

Internal problem ID [6775]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary problems. Page 132
Problem number : 25
Date solved : Sunday, March 30, 2025 at 11:22:20 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x) = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{4}}{12}+x^{2}-\frac {x^{3}}{3}+{\mathrm e}^{-x} c_1 +c_2 x +c_3 \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 37

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

\[ y(x)\to \frac {x^4}{12}-\frac {x^3}{3}+x^2+c_3 x+c_1 e^{-x}+c_2 \]

✓ Sympy. Time used: 0.137 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{- x} + \frac {x^{4}}{12} - \frac {x^{3}}{3} + x^{2} \]