75.10.2 problem 233

Internal problem ID [16849]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 9. The Riccati equation. Exercises page 75
Problem number : 233
Date solved : Tuesday, January 28, 2025 at 09:34:52 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }+y^{2}-2 y \sin \left (x \right )+\sin \left (x \right )^{2}-\cos \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

dsolve(diff(y(x),x)+y(x)^2-2*y(x)*sin(x)+sin(x)^2-cos(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.244 (sec). Leaf size: 20

DSolve[D[y[x],x]+y[x]^2-2*y[x]*Sin[x]+Sin[x]^2-Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sin (x)+\frac {1}{x+c_1} \\ y(x)\to \sin (x) \\ \end{align*}