58.1.37 problem 37

Internal problem ID [9108]
Book : Second order enumerated odes
Section : section 1
Problem number : 37
Date solved : Monday, January 27, 2025 at 05:42:05 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+y^{\prime }&=\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)+diff(y(x),x)=cos(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 28

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

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