3.3 problem 23 (e)

Internal problem ID [5264]

Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number: 23 (e).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 16

dsolve((x+y(x)*cos(x))+sin(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {-\frac {x^{2}}{2}+c_{1}}{\sin \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 19

DSolve[(x+y[x]*Cos[x])+Sin[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} \left (x^2-2 c_1\right ) \csc (x) \]