83.5.12 problem 12

Internal problem ID [19107]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 12:57:04 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(x),x)+2/x*y(x)=sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 26

DSolve[D[y[x],x]+2/x*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-\left (x^2-2\right ) \cos (x)+2 x \sin (x)+c_1}{x^2} \]