60.2.115 problem 691

Internal problem ID [10702]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 691
Date solved : Monday, January 27, 2025 at 09:28:24 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{3}+x^{3}}{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 17

dsolve(diff(y(x),x) = 1/2*(-sin(2*y(x))+cos(2*y(x))*x^3+x^3)/x,y(x), singsol=all)
 

\[ y = \arctan \left (\frac {x^{4}+8 c_{1}}{4 x}\right ) \]

✓ Solution by Mathematica

Time used: 3.312 (sec). Leaf size: 55

DSolve[D[y[x],x] == (x^3/2 + (x^3*Cos[2*y[x]])/2 - Sin[2*y[x]]/2)/x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \arctan \left (\frac {x^4+2 c_1}{4 x}\right ) \\ y(x)\to -\frac {1}{2} \pi \sqrt {\frac {1}{x^2}} x \\ y(x)\to \frac {1}{2} \pi \sqrt {\frac {1}{x^2}} x \\ \end{align*}