Internal problem ID [7466]
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]]
\[ \boxed {\cos \left (x \right ) y^{\prime \prime }+y^{\prime } \sin \left (x \right )-2 \cos \left (x \right )^{3} y=2 \cos \left (x \right )^{5}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \sinh \left (\sin \left (x \right ) \sqrt {2}\right ) c_{2} +\cosh \left (\sin \left (x \right ) \sqrt {2}\right ) c_{1} +\frac {1}{2}-\frac {\cos \left (2 x \right )}{2} \]
✓ Solution by Mathematica
Time used: 17.301 (sec). Leaf size: 167
DSolve[Cos[x]*y''[x]+Sin[x]*y'[x]-2*y[x]*Cos[x]^3==2*Cos[x]^5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos \left (\sqrt {-\cos (2 x)-1} \tan (x)\right ) \int _1^x\cos ^2(K[1]) \sqrt {-\cos (2 K[1])-1} \sin \left (\sqrt {-\cos (2 K[1])-1} \tan (K[1])\right )dK[1]+\sin \left (\sqrt {-\cos (2 x)-1} \tan (x)\right ) \int _1^x-\cos ^2(K[2]) \sqrt {-\cos (2 K[2])-1} \cos \left (\sqrt {-\cos (2 K[2])-1} \tan (K[2])\right )dK[2]+c_1 \cos \left (\sqrt {-\cos (2 x)-1} \tan (x)\right )+c_2 \sin \left (\sqrt {-\cos (2 x)-1} \tan (x)\right ) \]