Internal problem ID [12446]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number: 7.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(36*diff(y(x),x$4)-12*diff(y(x),x$3)-11*diff(y(x),x$2)+2*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x}{3}}+c_{2} {\mathrm e}^{-\frac {x}{3}} x +c_{3} {\mathrm e}^{\frac {x}{2}}+c_{4} {\mathrm e}^{\frac {x}{2}} x \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 41
DSolve[36*y''''[x]-12*y'''[x]-11*y''[x]+2*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/3} \left (c_3 e^{5 x/6}+x \left (c_4 e^{5 x/6}+c_2\right )+c_1\right ) \]