60.3.427 problem 1433

Internal problem ID [11437]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1433
Date solved : Tuesday, January 28, 2025 at 06:06:04 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }&=-\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 28

dsolve(diff(diff(y(x),x),x) = -sin(x)/cos(x)*diff(y(x),x)-1/4*(2*x^2+x^2*sin(x)^2-24*cos(x)^2)/x^2/cos(x)^2*y(x)+cos(x)^(1/2),y(x), singsol=all)
 

\[ y = \frac {\sqrt {\cos \left (x \right )}\, \left (4 c_{1} x^{5}-x^{4}+4 c_{2} \right )}{4 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.133 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}] == Sqrt[Cos[x]] - (Sec[x]^2*(2*x^2 - 24*Cos[x]^2 + x^2*Sin[x]^2)*y[x])/(4*x^2) - Tan[x]*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (4 c_2 x^5-5 x^4+20 c_1\right ) \sqrt {\cos (x)}}{20 x^2} \]