Internal problem ID [10589]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page
37
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_Abel, `2nd type`, `class B`]]
\[ \boxed {2 y \sin \left (x \right ) \cos \left (x \right )+y^{2} \sin \left (x \right )+\left (\sin \left (x \right )^{2}-2 y \cos \left (x \right )\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.359 (sec). Leaf size: 24
dsolve([(2*y(x)*sin(x)*cos(x)+y(x)^2*sin(x))+(sin(x)^2-2*y(x)*cos(x))*diff(y(x),x)=0,y(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\sin \left (x \right )^{2}+\sqrt {\sin \left (x \right )^{4}+36 \cos \left (x \right )}\right ) \sec \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 1.267 (sec). Leaf size: 32
DSolve[{(2*y[x]*Sin[x]*Cos[x]+y[x]^2*Sin[x])+(Sin[x]^2-2*y[x]*Cos[x])*y'[x]==0,{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \sec (x) \left (-\cos ^2(x)+\sqrt {\sin ^4(x)+36 \cos (x)}+1\right ) \\ \end{align*}