Internal problem ID [15043]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } \sin \left (x \right )-y \cos \left (x \right )=-\frac {\sin \left (x \right )^{2}}{x^{2}}} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {\sin \left (x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 19
DSolve[{y'[x]*Sin[x]-y[x]*Cos[x]==-Sin[x]^2/x^2,{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (x) \left (\text {Interval}[\{0,\text {Indeterminate}\},\{\text {Indeterminate},0\}]+\frac {1}{x}\right ) \]