15.14.22 problem 22

Internal problem ID [3194]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 22
Date solved : Sunday, March 30, 2025 at 01:20:55 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 43

ode:=diff(diff(diff(y(x),x),x),x)-diff(y(x),x) = exp(x)*(sin(x)-x^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -{\mathrm e}^{-x} c_2 +\frac {\left (-20 x^{3}+90 x^{2}-210 x +120 c_1 -12 \cos \left (x \right )-36 \sin \left (x \right )+225\right ) {\mathrm e}^{x}}{120}+c_3 \]

✓ Mathematica. Time used: 0.755 (sec). Leaf size: 63

ode=D[y[x],{x,3}]-D[y[x],x]==Exp[x]*(Sin[x]-x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{24} e^x \left (-4 x^3+18 x^2-42 x+45\right )-\frac {3}{10} e^x \sin (x)-\frac {1}{10} e^x \cos (x)+c_1 e^x-c_2 e^{-x}+c_3 \]

✓ Sympy. Time used: 0.319 (sec). Leaf size: 42

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

\[ y{\left (x \right )} = C_{1} + C_{3} e^{- x} + \left (C_{2} - \frac {x^{3}}{6} + \frac {3 x^{2}}{4} - \frac {7 x}{4} - \frac {3 \sin {\left (x \right )}}{10} - \frac {\cos {\left (x \right )}}{10}\right ) e^{x} \]