75.6.17 problem 150

Internal problem ID [16773]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 150
Date solved : Tuesday, January 28, 2025 at 09:22:03 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\infty \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 10

dsolve([diff(y(x),x)*sin(x)-y(x)*cos(x)=-sin(x)^2/x^2,y(infinity) = 0],y(x), singsol=all)
 

\[ y = \frac {\sin \left (x \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 19

DSolve[{D[y[x],x]*Sin[x]-y[x]*Cos[x]==-Sin[x]^2/x^2,{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (x) \left (\text {Interval}[\{0,\text {Indeterminate}\},\{\text {Indeterminate},0\}]+\frac {1}{x}\right ) \]