60.1.277 problem 278

Internal problem ID [10291]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 278
Date solved : Monday, January 27, 2025 at 06:50:39 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (y^{2}+4 \sin \left (x \right )\right ) y^{\prime }-\cos \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 28

dsolve((y(x)^2+4*sin(x))*diff(y(x),x)-cos(x)=0,y(x), singsol=all)
 

\[ \frac {\left (-8 y^{2}-4 y-32 \sin \left (x \right )-1\right ) {\mathrm e}^{-4 y}}{32}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.187 (sec). Leaf size: 83

DSolve[(y[x]^2+4*Sin[x])*D[y[x],x]-Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^x-e^{-4 y(x)} \cos (K[1])dK[1]+\int _1^{y(x)}\left (e^{-4 K[2]} K[2]^2-e^{-4 K[2]} \left (e^{4 K[2]} \int _1^x4 e^{-4 K[2]} \cos (K[1])dK[1]-4 \sin (x)\right )\right )dK[2]=c_1,y(x)\right ] \]