56.1.42 problem 42

Internal problem ID [8754]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 42
Date solved : Monday, January 27, 2025 at 04:46:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 32

dsolve(diff(y(x),x$2)+diff(y(x),x)+4*y(x)=1,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {15}\, x}{2}\right ) c_{2} +{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {15}\, x}{2}\right ) c_{1} +\frac {1}{4} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 51

DSolve[D[y[x],{x,2}]+D[y[x],x]+4*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 e^{-x/2} \cos \left (\frac {\sqrt {15} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {15} x}{2}\right )+\frac {1}{4} \]