60.4.66 problem 1516

Internal problem ID [11517]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1516
Date solved : Tuesday, January 28, 2025 at 06:06:43 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 188

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+(x+3)*x^2*diff(diff(y(x),x),x)+5*(x-6)*x*diff(y(x),x)+(4*x+30)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-x} c_3 \left (x^{8}+28 x^{7}+450 x^{6}+5100 x^{5}+42900 x^{4}+267120 x^{3}+1179360 x^{2}+3326400 x +4536000\right ) \operatorname {Ei}_{1}\left (-x \right )+c_{2} {\mathrm e}^{-x} \left (x^{8}+28 x^{7}+450 x^{6}+5100 x^{5}+42900 x^{4}+267120 x^{3}+1179360 x^{2}+3326400 x +4536000\right )+60 c_3 \left (x^{4}-84 x^{3}+2016 x^{2}-20160 x +75600\right ) \ln \left (x \right )+c_3 \,x^{7}+29 c_3 \,x^{6}+480 c_3 \,x^{5}+\left (c_{1} +5612 c_3 \right ) x^{4}+\left (-84 c_{1} +40152 c_3 \right ) x^{3}+\left (2016 c_{1} +654192 c_3 \right ) x^{2}+\left (-20160 c_{1} -2761920 c_3 \right ) x +75600 c_{1} [phone] c_3}{x^{6}} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(30 + 4*x)*y[x] + 5*(-6 + x)*x*D[y[x],x] + x^2*(3 + x)*D[y[x],{x,2}] + x^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out