Internal problem ID [15168]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 306.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-\cos \left (\ln \left (y\right )\right ) y^{\prime }=-\sin \left (\ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 81
dsolve(sin(ln(x))-cos(ln(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-2 \cos \left (\ln \left (x \right )\right ) x^{2} \sin \left (\ln \left (x \right )\right )-2 \sin \left (\ln \left (x \right )\right ) \sin \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z}} x +2 \sin \left (\textit {\_Z} \right ) \cos \left (\ln \left (x \right )\right ) {\mathrm e}^{\textit {\_Z}} x -2 \,{\mathrm e}^{2 \textit {\_Z}} \cos \left (\textit {\_Z} \right )^{2}+4 c_{1} x \sin \left (\ln \left (x \right )\right )-4 \cos \left (\ln \left (x \right )\right ) c_{1} x -4 \sin \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z}} c_{1} +4 c_{1}^{2}+x^{2}+{\mathrm e}^{2 \textit {\_Z}}\right )} \]
✓ Solution by Mathematica
Time used: 0.386 (sec). Leaf size: 47
DSolve[Sin[Log[x]]-Cos[Log[y[x]]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sin (\log (\text {$\#$1}))+\frac {1}{2} \text {$\#$1} \cos (\log (\text {$\#$1}))\&\right ]\left [\frac {1}{2} x \sin (\log (x))-\frac {1}{2} x \cos (\log (x))+c_1\right ] \]