71.4.18 problem 18

Internal problem ID [14390]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 06:29:23 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.065 (sec). Leaf size: 16

dsolve([diff(y(x),x)=y(x)/x+cos(x),y(-1) = 0],y(x), singsol=all)
 

\[ y = \left (\operatorname {Ci}\left (x \right )-\operatorname {Ci}\left (1\right )-i \pi \right ) x \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 14

DSolve[{D[y[x],x]==y[x]/x+Cos[x],{y[-1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (\operatorname {CosIntegral}(x)-\operatorname {CosIntegral}(-1)) \]