60.4.27 problem 1475

Internal problem ID [11478]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1475
Date solved : Monday, January 27, 2025 at 11:22:32 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y+18 \,{\mathrm e}^{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(4*diff(diff(diff(y(x),x),x),x)-8*diff(diff(y(x),x),x)-11*diff(y(x),x)-3*y(x)+18*exp(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 37

DSolve[18*E^x - 3*y[x] - 11*D[y[x],x] - 8*D[y[x],{x,2}] + 4*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/2} \left (e^{3 x/2}+c_2 x+c_3 e^{7 x/2}+c_1\right ) \]