Internal problem ID [4271]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR
FIRST-ORDER EQUATIONS. page 406
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\cos \left (x \right ) \cos \left (y\right )+\sin \left (x \right )^{2}-\left (\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right )^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.438 (sec). Leaf size: 35
dsolve((cos(x)*cos(y(x))+sin(x)^2)-(sin(x)*sin(y(x))+cos(y(x))^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1} +x -y \left (x \right )-\frac {\sin \left (2 x \right )}{2}+\sin \left (x +y \left (x \right )\right )+\sin \left (-y \left (x \right )+x \right )-\frac {\sin \left (2 y \left (x \right )\right )}{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.38 (sec). Leaf size: 43
DSolve[(Cos[x]*Cos[y[x]]+Sin[x]^2)-(Sin[x]*Sin[y[x]]+Cos[y[x]]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \left (\frac {y(x)}{2}+\frac {1}{4} \sin (2 y(x))\right )-2 \sin (x) \cos (y(x))-x+\frac {1}{2} \sin (2 x)=c_1,y(x)\right ] \]