60.1.90 problem 90

Internal problem ID [10104]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 90
Date solved : Monday, January 27, 2025 at 06:27:39 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 25

DSolve[x*D[y[x],x]+ y[x] - x*Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\int _1^xK[1] \sin (K[1])dK[1]+c_1}{x} \]