75.12.2 problem 276

Internal problem ID [16868]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 276
Date solved : Tuesday, January 28, 2025 at 09:36:00 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.346 (sec). Leaf size: 34

DSolve[x*Sin[x]*D[y[x],x]+(Sin[x]-x*Cos[x])*y[x]==Sin[x]*Cos[x]-x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin (x) \left (\int _1^x\left (\cot (K[1])-\csc ^2(K[1]) K[1]\right )dK[1]+c_1\right )}{x} \]