60.2.420 problem 997

Internal problem ID [11007]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 997
Date solved : Monday, January 27, 2025 at 10:40:22 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.172 (sec). Leaf size: 26

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

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