Internal problem ID [12209]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-a^{4} y=5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(x),x$4)-a^4*y(x)=5*a^4*exp(a*x)*sin(a*x),y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{a x} \sin \left (a x \right )+c_{1} \cos \left (a x \right )+c_{2} {\mathrm e}^{a x}+c_{3} \sin \left (a x \right )+c_{4} {\mathrm e}^{-a x} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 45
DSolve[y''''[x]-a^4*y[x]==5*a^4*Exp[a*x]*Sin[a*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 e^{-a x}+c_4 e^{a x}+c_1 \cos (a x)+\left (-e^{a x}+c_3\right ) \sin (a x) \]