60.1.195 problem 196

Internal problem ID [10209]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 196
Date solved : Monday, January 27, 2025 at 06:38:37 PM
CAS classification : [_linear]

\begin{align*} \cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

dsolve(cos(x)*diff(y(x),x) + y(x) + (1 + sin(x))*cos(x)=0,y(x), singsol=all)
 

\[ y = \frac {-2 \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+2 \ln \left (\cos \left (x \right )\right )+\sin \left (x \right )+c_{1}}{\sec \left (x \right )+\tan \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.784 (sec). Leaf size: 46

DSolve[Cos[x]*D[y[x],x] + y[x] + (1 + Sin[x])*Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} \left (\int _1^x-e^{2 \text {arctanh}\left (\tan \left (\frac {K[1]}{2}\right )\right )} (\sin (K[1])+1)dK[1]+c_1\right ) \]