Internal problem ID [9126]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1547.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+6 f y^{\prime \prime \prime }+\left (11 f^{2}+4 \mathit {df} +10 g \right ) y^{\prime \prime }+\left (6 f^{3}+7 f \mathit {df} +30 f g +\mathit {ddf} +10 \mathit {dg} \right ) y^{\prime }+3 \left (6 f^{2} g +2 \mathit {df} g +5 \mathit {dg} f +3 g^{2}+\mathit {ddg} \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 87
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+6*f*diff(diff(diff(y(x),x),x),x)+(11*f^2+4*df+10*g)*diff(diff(y(x),x),x)+(6*f^3+7*df*f+30*f*g+ddf+10*dg)*diff(y(x),x)+3*(6*f^2*g+2*df*g+5*dg*f+3*g^2+ddg)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+6 f \,\textit {\_Z}^{3}+\left (11 f^{2}+4 \mathit {df} +10 g \right ) \textit {\_Z}^{2}+\left (6 f^{3}+7 \mathit {df} f +30 f g +\mathit {ddf} +10 \mathit {dg} \right ) \textit {\_Z} +18 f^{2} g +6 \mathit {df} g +15 \mathit {dg} f +9 g^{2}+3 \mathit {ddg} , \mathit {index} =\textit {\_a} \right ) x} \textit {\_C}_{\textit {\_a}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]*(6*f[x]^3 + 30*f[x]*g[x] + 7*f[x]*Derivative[1][f][x] + 10*Derivative[1][g][x] + Derivative[2][f][x]) + 3*y[x]*(6*f[x]^2*g[x] + 3*g[x]^2 + 2*g[x]*Derivative[1][f][x] + 5*f[x]*Derivative[1][g][x] + Derivative[2][g][x]) + (11*f[x]^2 + 10*g[x] + 4*Derivative[1][f][x])*y''[x] + 6*f[x]*Derivative[3][y][x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved