60.4.69 problem 1519

Internal problem ID [11520]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1519
Date solved : Tuesday, January 28, 2025 at 06:06:43 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 19

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

\[ y = c_{2} x^{3}+c_{1} x^{2}+x c_3 +c_3 \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 58

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

\[ y(x)\to \frac {1}{8} \left (2 c_1 \left (x^3-3 x^2+3 x+3\right )-(x-1) \left (4 c_2 \left (x^2-2 x-1\right )+c_3 \left (-3 x^2+2 x+1\right )\right )\right ) \]