Internal problem ID [9154]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1575.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime } \left (\sin ^{6}\relax (x )\right )+4 y^{\prime \prime \prime } \left (\sin ^{5}\relax (x )\right ) \cos \relax (x )-6 y^{\prime \prime } \left (\sin ^{6}\relax (x )\right )-4 y^{\prime } \left (\sin ^{5}\relax (x )\right ) \cos \relax (x )+y \left (\sin ^{6}\relax (x )\right )-f=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 1055
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)*sin(x)^6+4*diff(diff(diff(y(x),x),x),x)*sin(x)^5*cos(x)-6*diff(diff(y(x),x),x)*sin(x)^6-4*diff(y(x),x)*sin(x)^5*cos(x)+y(x)*sin(x)^6-f=0,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 5.396 (sec). Leaf size: 119
DSolve[-f[x] + Sin[x]^6*y[x] - 4*Cos[x]*Sin[x]^5*y'[x] - 6*Sin[x]^6*y''[x] + 4*Cos[x]*Sin[x]^5*Derivative[3][y][x] + Sin[x]^6*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \csc (x) \left (\int _1^x-\frac {1}{6} \csc ^5(K[1]) f(K[1]) K[1]^3dK[1]+x \left (\int _1^x\frac {1}{2} \csc ^5(K[2]) f(K[2]) K[2]^2dK[2]+x \left (x \int _1^x\frac {1}{6} \csc ^5(K[4]) f(K[4])dK[4]+\int _1^x-\frac {1}{2} \csc ^5(K[3]) f(K[3]) K[3]dK[3]\right )\right )+x (x (c_4 x+c_3)+c_2)+c_1\right ) \\ \end{align*}