Internal problem ID [6710]
Book: Second order enumerated odes
Section: section 2
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\cos \relax (x ) y^{\prime \prime }+\sin \relax (x ) y^{\prime }-2 y \left (\cos ^{3}\relax (x )\right )-2 \left (\cos ^{5}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 30
dsolve(cos(x)*diff(y(x),x$2)+sin(x)*diff(y(x),x)-2*y(x)*cos(x)^3=2*cos(x)^5,y(x), singsol=all)
\[ y \relax (x ) = \sinh \left (\sqrt {2}\, \sin \relax (x )\right ) c_{2}+\cosh \left (\sqrt {2}\, \sin \relax (x )\right ) c_{1}+\frac {1}{2}-\frac {\cos \left (2 x \right )}{2} \]
✓ Solution by Mathematica
Time used: 7.416 (sec). Leaf size: 132
DSolve[Cos[x]*y''[x]+Sin[x]*y'[x]-2*y[x]*Cos[x]^3==2*Cos[x]^5,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin \left (\sqrt {-\cos (2 x)-1} \tan (x)\right ) \left (\int _1^x\sqrt {2} \left (-\cos ^2(K[2])\right )^{3/2} \cos \left (\sqrt {-\cos (2 K[2])-1} \tan (K[2])\right )dK[2]+c_2\right )+\cos \left (\sqrt {-\cos (2 x)-1} \tan (x)\right ) \left (\int _1^x\cos ^2(K[1]) \sqrt {-\cos (2 K[1])-1} \sin \left (\sqrt {-\cos (2 K[1])-1} \tan (K[1])\right )dK[1]+c_1\right ) \\ \end{align*}