60.4.21 problem 1469

Internal problem ID [11472]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1469
Date solved : Tuesday, January 28, 2025 at 06:06:33 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+3 a x y^{\prime \prime }+3 a^{2} x^{2} y^{\prime }+a^{3} x^{3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 46

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

\[ y = {\mathrm e}^{-\frac {x \left (2 \sqrt {3}\, \sqrt {a}+a x \right )}{2}} \left (c_{2} {\mathrm e}^{2 \sqrt {3}\, \sqrt {a}\, x}+c_{1} {\mathrm e}^{\sqrt {3}\, \sqrt {a}\, x}+c_3 \right ) \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 68

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

\[ y(x)\to e^{-\frac {a x^2}{2}-\sqrt {3} \sqrt {a} x} \left (c_1 e^{\sqrt {3} \sqrt {a} x}+c_3 e^{2 \sqrt {3} \sqrt {a} x}+c_2\right ) \]