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]
\[ \boxed {y \cos \left (x \right )+\sin \left (x \right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((x+y(x)*cos(x))+sin(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (x^{2}-2 c_{1} \right ) \csc \left (x \right )}{2} \]
✓ 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]
\[ y(x)\to -\frac {1}{2} \left (x^2-2 c_1\right ) \csc (x) \]