18.1.2 problem Problem 14.2 (b)

Internal problem ID [3458]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.2 (b)
Date solved : Monday, January 27, 2025 at 07:37:26 AM
CAS classification : [_separable]

\begin{align*} \frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 19

dsolve(diff(y(x),x)/tan(x)-y(x)/(1+x^2)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{\int \frac {\tan \left (x \right )}{x^{2}+1}d x} \]

✓ Solution by Mathematica

Time used: 9.503 (sec). Leaf size: 34

DSolve[D[y[x],x]/Tan[x]-y[x]/(1+x^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \exp \left (\int _1^x\frac {\tan (K[1])}{K[1]^2+1}dK[1]\right ) \\ y(x)\to 0 \\ \end{align*}