71.4.19 problem 19

Internal problem ID [14391]
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 : 19
Date solved : Tuesday, January 28, 2025 at 06:29:25 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.464 (sec). Leaf size: 18

dsolve([diff(y(x),x)=y(x)/x+tan(x),y(Pi) = 0],y(x), singsol=all)
 

\[ y = \left (\int _{\pi }^{x}\frac {\tan \left (\textit {\_z1} \right )}{\textit {\_z1}}d \textit {\_z1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 22

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

\[ y(x)\to x \int _{\pi }^x\frac {\tan (K[1])}{K[1]}dK[1] \]