60.4.42 problem 1490

Internal problem ID [11493]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1490
Date solved : Monday, January 27, 2025 at 11:22:39 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 18

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

\[ y = c_{1} +c_{2} x \operatorname {BesselJ}\left (1, x\right )+c_3 x \operatorname {BesselY}\left (1, x\right ) \]

✓ Solution by Mathematica

Time used: 60.026 (sec). Leaf size: 33

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

\[ y(x)\to \int _1^x(\operatorname {BesselJ}(0,K[1]) c_1+\operatorname {BesselY}(0,K[1]) c_2) K[1]dK[1]+c_3 \]