60.5.38 problem 1573

Internal problem ID [11572]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1573
Date solved : Monday, January 27, 2025 at 11:23:34 PM
CAS classification : [[_high_order, _fully, _exact, _linear]]

\begin{align*} \left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{x}-\frac {1}{x^{5}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 41

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)
 

\[ y = \frac {24 c_{1} x^{4}+24 c_{2} x^{3}+24 x^{2} c_3 +24 c_4 x +1}{24 \left ({\mathrm e}^{x}+2 x \right ) x} \]

✓ Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 48

DSolve[-x^(-5) + E^x*y[x] + 4*E^x*D[y[x],x] + 6*E^x*D[y[x],{x,2}] + 4*(2 + E^x)*Derivative[3][y][x] + (E^x + 2*x)*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {24 c_4 x^4+24 c_3 x^3+24 c_2 x^2+24 c_1 x+1}{48 x^2+24 e^x x} \]