Internal problem ID [7086]
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]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+4 y=1} \]
✓ 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)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {15}\, x}{2}\right ) c_{2} +{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {15}\, x}{2}\right ) c_{1} +\frac {1}{4} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 51
DSolve[y''[x]+y'[x]+4*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 e^{-x/2} \cos \left (\frac {\sqrt {15} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {15} x}{2}\right )+\frac {1}{4} \]