Internal problem ID [1048]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {-4 \cos \relax (x ) y+4 \cos \relax (x ) \sin \relax (x )+\sec ^{2}\relax (x )+\left (4 y-4 \sin \relax (x )\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 1.854 (sec). Leaf size: 40
dsolve([(-4*y(x)*cos(x)+4*sin(x)*cos(x)+sec(x)^2)+(4*y(x)-4*sin(x))*diff(y(x),x)=0,y(1/4*Pi) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {2 \left (\cos ^{2}\relax (x )\right ) \sin \relax (x )-\sqrt {2}\, \sqrt {\left (\cos ^{3}\relax (x )\right ) \left (2 \cos \relax (x )-\sin \relax (x )\right )}}{2 \cos \relax (x )^{2}} \]
✓ Solution by Mathematica
Time used: 1.693 (sec). Leaf size: 38
DSolve[{(-4*y[x]*Cos[x]+4*Sin[x]*Cos[x]+Sec[x]^2)+(4*y[x]-4*Sin[x])*y'[x]==0,y[Pi/4]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (x)+\frac {1}{2} \sqrt {-\sec ^2(x)} \sqrt {\sin (2 x)-2 \cos (2 x)-2} \\ \end{align*}