15.8.10 problem 10

Internal problem ID [3013]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:07:49 AM
CAS classification : [_exact]

\begin{align*} y \sin \left (x \right )-2 \cos \left (y\right )+\tan \left (x \right )-\left (\cos \left (x \right )-2 x \sin \left (y\right )+\sin \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 25

dsolve((y(x)*sin(x)-2*cos(y(x))+tan(x) )-(cos(x)-2*x*sin(y(x))+sin(y(x)) )*diff(y(x),x)=0,y(x), singsol=all)
 

\[ -\cos \left (x \right ) y-2 x \cos \left (y\right )-\ln \left (\cos \left (x \right )\right )+\cos \left (y\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.702 (sec). Leaf size: 29

DSolve[(y[x]*Sin[x]-2*Cos[y[x]]+Tan[x] )-(Cos[x]-2*x*Sin[y[x]]+Sin[y[x]] )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[4 x \cos (y(x))-2 \cos (y(x))+2 y(x) \cos (x)+2 \log (\cos (x))=c_1,y(x)] \]