Internal problem ID [12210]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 160.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y=8 \cos \left (a x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(diff(y(x),x$4)+2*a^2*diff(y(x),x$2)+a^4*y(x)=8*cos(a*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (a^{2} x^{2}-2\right ) \cos \left (a x \right )}{a^{4}}+\frac {3 \sin \left (a x \right ) x}{a^{3}}+c_{1} \cos \left (a x \right )+c_{2} \sin \left (a x \right )+c_{3} \cos \left (a x \right ) x +c_{4} \sin \left (a x \right ) x \]
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 64
DSolve[y''''[x]+2*a^2*y''[x]+a^4*y[x]==8*Cos[a*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 a \left (x \left (2+a^3 c_4\right )+a^3 c_3\right ) \sin (a x)+\left (2 a^4 (c_2 x+c_1)-2 a^2 x^2+5\right ) \cos (a x)}{2 a^4} \]