60.4.23 problem 1471

Internal problem ID [11474]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1471
Date solved : Tuesday, January 28, 2025 at 06:06:33 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime }+f \left (x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 33

dsolve(diff(diff(diff(y(x),x),x),x)+f(x)*diff(diff(y(x),x),x)+diff(y(x),x)+f(x)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{i x} \left (\int {\mathrm e}^{-2 i x} \left (c_3 \left (\int {\mathrm e}^{\int \left (-f+i\right )d x}d x \right )+c_{2} \right )d x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 84

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

\[ y(x)\to c_3 e^{i x} \int _1^xe^{-2 i K[3]} \int _1^{K[3]}\exp \left (\int _1^{K[2]}(i-f(K[1]))dK[1]\right )dK[2]dK[3]+c_1 e^{i x}+\frac {1}{2} i c_2 e^{-i x} \]