4.19 problem 19

Internal problem ID [72]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 19.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

\[ \boxed {y \cot \left (x \right )+y^{\prime }=\cos \left (x \right )} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 19

dsolve(cot(x)*y(x)+diff(y(x),x) = cos(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\left (2 \cos \left (x \right )^{2}-4 c_{1} -1\right ) \csc \left (x \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 19

DSolve[Cot[x]*y[x]+y'[x] == Cos[x],y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to -\frac {1}{2} \cos (x) \cot (x)+c_1 \csc (x) \]