Internal problem ID [11261]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 45. Roots of
auxiliary equation complex. Page 95
Problem number: Ex 2.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (x \right )+c_{2} \cos \left (x \right )+c_{3} \sin \left (x \right ) x +c_{4} \cos \left (x \right ) x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 26
DSolve[y''''[x]+2*y''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (c_2 x+c_1) \cos (x)+(c_4 x+c_3) \sin (x) \]