60.4.18 problem 1466

Internal problem ID [11469]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1466
Date solved : Monday, January 27, 2025 at 11:22:27 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{a x} \left (\frac {1}{6} x^{3}+c_{1} +c_{2} x +x^{2} c_3 \right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{6} e^{a x} \left (x^3+6 c_3 x^2+6 c_2 x+6 c_1\right ) \]