60.3.413 problem 1419

Internal problem ID [11423]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1419
Date solved : Monday, January 27, 2025 at 11:20:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {\left (\sin \left (x \right ) x^{2}-2 \cos \left (x \right ) x \right ) y^{\prime }}{x^{2} \cos \left (x \right )}-\frac {\left (2 \cos \left (x \right )-x \sin \left (x \right )\right ) y}{x^{2} \cos \left (x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.273 (sec). Leaf size: 12

dsolve(diff(diff(y(x),x),x) = -(sin(x)*x^2-2*cos(x)*x)/x^2/cos(x)*diff(y(x),x)-(2*cos(x)-x*sin(x))/x^2/cos(x)*y(x),y(x), singsol=all)
 

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],{x,2}] == -((Sec[x]*(2*x*Cos[x] - x*Sin[x])*y[x])/x^2) - (Sec[x]*(-2*x*Cos[x] + x^2*Sin[x])*D[y[x],x])/x^2,y[x],x,IncludeSingularSolutions -> True]
 

Not solved