Internal problem ID [12515]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 145.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x$4)-8*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{4} x +c_{3} \right ) {\mathrm e}^{-2 x}+{\mathrm e}^{2 x} \left (c_{2} x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 35
DSolve[y''''[x]-8*y''[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_3 e^{4 x}+x \left (c_4 e^{4 x}+c_2\right )+c_1\right ) \]