60.4.63 problem 1513

Internal problem ID [11514]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1513
Date solved : Tuesday, January 28, 2025 at 06:06:42 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+\left (x^{2}+8\right ) x y^{\prime }-2 \left (x^{2}+4\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 18

dsolve(x^3*diff(diff(diff(y(x),x),x),x)-4*x^2*diff(diff(y(x),x),x)+(x^2+8)*x*diff(y(x),x)-2*(x^2+4)*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_3 \cos \left (x \right )+\sin \left (x \right ) c_{2} +c_{1} x \right ) \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 40

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

\[ y(x)\to x^2 \left (c_2 \int _1^xj_1(K[1])dK[1]+c_3 \int _1^xy_1(K[2])dK[2]+c_1\right ) \]