35.3.12 problem 12

Internal problem ID [6116]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 12
Date solved : Monday, January 27, 2025 at 01:36:27 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 10

dsolve(diff(x(y),y)=cos(y)-x(y)*tan(y),x(y), singsol=all)
 

\[ x \left (y \right ) = \left (y +c_1 \right ) \cos \left (y \right ) \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 12

DSolve[D[x[y],y]==Cos[y]-x[y]*Tan[y],x[y],y,IncludeSingularSolutions -> True]
 

\[ x(y)\to (y+c_1) \cos (y) \]