63.1.112 problem 159

Internal problem ID [15552]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 159
Date solved : Thursday, October 02, 2025 at 10:19:48 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 37

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-a^4*y(x) = 5*a^4*exp(a*x)*sin(a*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_4 \,{\mathrm e}^{-a x}+\left (-\sin \left (a x \right )+c_2 \right ) {\mathrm e}^{a x}+c_3 \sin \left (a x \right )+c_1 \cos \left (a x \right ) \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 45

ode=D[y[x],{x,4}]-a^4*y[x]==5*a^4*Exp[a*x]*Sin[a*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 e^{-a x}+c_4 e^{a x}+c_1 \cos (a x)+\left (-e^{a x}+c_3\right ) \sin (a x) \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a**4*y(x) - 5*a**4*exp(a*x)*sin(a*x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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