60.4.76 problem 1526

Internal problem ID [11527]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1526
Date solved : Tuesday, January 28, 2025 at 06:06:46 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (x^{4}+2 x^{2}+2 x +1\right ) y^{\prime \prime \prime }-\left (2 x^{6}+3 x^{4}-6 x^{2}-6 x -1\right ) y^{\prime \prime }+\left (x^{6}-6 x^{3}-15 x^{2}-12 x -2\right ) y^{\prime }+\left (x^{4}+4 x^{3}+8 x^{2}+6 x +1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 19

dsolve(x^2*(x^4+2*x^2+2*x+1)*diff(diff(diff(y(x),x),x),x)-(2*x^6+3*x^4-6*x^2-6*x-1)*diff(diff(y(x),x),x)+(x^6-6*x^3-15*x^2-12*x-2)*diff(y(x),x)+(x^4+4*x^3+8*x^2+6*x+1)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 130.219 (sec). Leaf size: 25

DSolve[(1 + 6*x + 8*x^2 + 4*x^3 + x^4)*y[x] + (-2 - 12*x - 15*x^2 - 6*x^3 + x^6)*D[y[x],x] - (-1 - 6*x - 6*x^2 + 3*x^4 + 2*x^6)*D[y[x],{x,2}] + x^2*(1 + 2*x + 2*x^2 + x^4)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (c_2 x+c_1)+c_3 e^{\frac {1}{x}} \]