60.4.24 problem 1472

Internal problem ID [11475]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1472
Date solved : Tuesday, January 28, 2025 at 06:06:34 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 85

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

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