Internal problem ID [9905]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1573.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _fully, _exact, _linear]]
\[ \boxed {\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 y^{\prime \prime } {\mathrm e}^{x}+4 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{x}=\frac {1}{x^{5}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 65
dsolve((exp(x)+2*x)*diff(diff(diff(diff(y(x),x),x),x),x)+4*(exp(x)+2)*diff(diff(diff(y(x),x),x),x)+6*exp(x)*diff(diff(y(x),x),x)+4*exp(x)*diff(y(x),x)+y(x)*exp(x)-1/x^5=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{4}}{{\mathrm e}^{x}+2 x}+\frac {c_{3} x}{{\mathrm e}^{x}+2 x}+\frac {1}{24 \left ({\mathrm e}^{x}+2 x \right ) x}+\frac {c_{1} x^{3}}{{\mathrm e}^{x}+2 x}+\frac {c_{2} x^{2}}{{\mathrm e}^{x}+2 x} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 48
DSolve[-x^(-5) + E^x*y[x] + 4*E^x*y'[x] + 6*E^x*y''[x] + 4*(2 + E^x)*Derivative[3][y][x] + (E^x + 2*x)*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {24 c_4 x^4+24 c_3 x^3+24 c_2 x^2+24 c_1 x+1}{48 x^2+24 e^x x} \]