75.6.35 problem 168

Internal problem ID [16791]
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 : 168
Date solved : Tuesday, January 28, 2025 at 09:23:05 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime } \cos \left (y\right )+\sin \left (y\right )&=1+x \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 17

dsolve(diff(y(x),x)*cos(y(x))+sin(y(x))=x+1,y(x), singsol=all)
 

\[ y = -\arcsin \left (-x +c_{1} {\mathrm e}^{-x}\right ) \]

✓ Solution by Mathematica

Time used: 27.910 (sec). Leaf size: 17

DSolve[D[y[x],x]*Cos[y[x]]+Sin[y[x]]==x+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (x-c_1 e^{-x}\right ) \]