Internal problem ID [6333]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }+4 y-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)+diff(y(x),x)+4*y(x)=1,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {15}\, x}{2}\right ) c_{2}+{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {15}\, x}{2}\right ) c_{1}+\frac {1}{4} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 46
DSolve[y''[x]+y'[x]+4*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4}+e^{-x/2} \left (c_2 \cos \left (\frac {\sqrt {15} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {15} x}{2}\right )\right ) \\ \end{align*}