1.90 problem 90

Internal problem ID [8427]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 90.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

\[ \boxed {x y^{\prime }+y=x \sin \left (x \right )} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 19

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

\[ y(x)\to \frac {\sin (x)-x \cos (x)+c_1}{x} \]