Internal problem ID [2170]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {2 y^{\prime \prime }+y^{\prime }=8 \sin \left (2 x \right )+{\mathrm e}^{-x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve([2*diff(y(x),x$2)+diff(y(x),x)=8*sin(2*x)+exp(-x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {98 \,{\mathrm e}^{-\frac {x}{2}}}{17}-\frac {16 \sin \left (2 x \right )}{17}+{\mathrm e}^{-x}-\frac {4 \cos \left (2 x \right )}{17}+6 \]
✓ Solution by Mathematica
Time used: 0.384 (sec). Leaf size: 39
DSolve[{2*y''[x]+y'[x]==8*Sin[2*x]+Exp[-x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x}-\frac {98 e^{-x/2}}{17}-\frac {16}{17} \sin (2 x)-\frac {4}{17} \cos (2 x)+6 \]