60.4.62 problem 1512

Internal problem ID [11513]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1512
Date solved : Monday, January 27, 2025 at 11:22:49 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+\left (-a^{2}+1\right ) x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)+(-a^2+1)*x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +c_{2} x^{a}+c_3 \,x^{-a} \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 29

DSolve[(1 - a^2)*x*D[y[x],x] + 3*x^2*D[y[x],{x,2}] + x^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-c_1 x^{-a}+c_2 x^a+a c_3}{a} \]