Internal problem ID [12784]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.5, page 221
Problem number: 4.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y=4+3 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 1, y^{\prime \prime \prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve([diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=3*x+4,y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 1, (D@@3)(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = 4+\left (x -4\right ) \cos \left (x \right )+\frac {\left (-3 x -8\right ) \sin \left (x \right )}{2}+3 x \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 27
DSolve[{y''''[x]+2*y''[x]+y[x]==3*x+4,{y[0]==0,y'[0]==0,y''[0]==1,y'''[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x-\frac {1}{2} (3 x+8) \sin (x)+(x-4) \cos (x)+4 \]