69.1.112 problem 159

Internal problem ID [14265]
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 : Tuesday, January 28, 2025 at 06:24:56 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*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 37

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

\[ y = c_4 \,{\mathrm e}^{-a x}+\left (c_{2} -\sin \left (a x \right )\right ) {\mathrm e}^{a x}+c_{1} \cos \left (a x \right )+c_{3} \sin \left (a x \right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 45

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

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