57.1.28 problem 28

Internal problem ID [9012]
Book : First order enumerated odes
Section : section 1
Problem number : 28
Date solved : Monday, January 27, 2025 at 05:27:15 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 10

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

\[ y = \left (\operatorname {Ci}\left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 12

DSolve[D[y[x],x]==Cos[x]+y[x]/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (\operatorname {CosIntegral}(x)+c_1) \]