60.3.87 problem 1091

Internal problem ID [11097]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1091
Date solved : Monday, January 27, 2025 at 10:45:38 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

dsolve(x*(diff(diff(y(x),x),x)+y(x))-cos(x)=0,y(x), singsol=all)
 

\[ y = \frac {\sin \left (x \right ) \operatorname {Ci}\left (2 x \right )}{2}-\frac {\operatorname {Si}\left (2 x \right ) \cos \left (x \right )}{2}+\frac {\left (2 c_{2} +\ln \left (x \right )\right ) \sin \left (x \right )}{2}+\cos \left (x \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 56

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

\[ y(x)\to \cos (x) \int _1^x-\frac {\cos (K[1]) \sin (K[1])}{K[1]}dK[1]+\frac {1}{2} \operatorname {CosIntegral}(2 x) \sin (x)+\frac {1}{2} \log (x) \sin (x)+c_1 \cos (x)+c_2 \sin (x) \]