Internal problem ID [1978]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {y^{\prime }}{\tan \relax (x )}-\frac {y}{x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 19
dsolve(diff(y(x),x)/tan(x)-y(x)/(1+x^2)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\int \frac {\tan \relax (x )}{x^{2}+1}d x} \]
✓ Solution by Mathematica
Time used: 5.178 (sec). Leaf size: 34
DSolve[y'[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*}