60.3.426 problem 1432

Internal problem ID [11436]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1432
Date solved : Monday, January 27, 2025 at 11:21:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

dsolve(diff(diff(y(x),x),x) = -1/sin(x)*cos(x)*diff(y(x),x)-1/4*(-17*sin(x)^2-1)/sin(x)^2*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}] == -1/4*(Csc[x]^2*(-1 - 17*Sin[x]^2)*y[x]) - Cot[x]*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-2 x} \left (c_2 e^{4 x}+4 c_1\right )}{4 \sqrt {\sin (x)}} \]