60.2.284 problem 860

Internal problem ID [10871]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 860
Date solved : Monday, January 27, 2025 at 10:19:12 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {-\sin \left (2 y\right )+x \cos \left (2 y\right )+\cos \left (2 y\right ) x^{3}+\cos \left (2 y\right ) x^{4}+x +x^{3}+x^{4}}{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 27

dsolve(diff(y(x),x) = 1/2*(-sin(2*y(x))+x*cos(2*y(x))+cos(2*y(x))*x^3+cos(2*y(x))*x^4+x+x^3+x^4)/x,y(x), singsol=all)
 

\[ y = \arctan \left (\frac {4 x^{5}+5 x^{4}+10 x^{2}+c_{1}}{20 x}\right ) \]

✓ Solution by Mathematica

Time used: 2.395 (sec). Leaf size: 69

DSolve[D[y[x],x] == (x/2 + x^3/2 + x^4/2 + (x*Cos[2*y[x]])/2 + (x^3*Cos[2*y[x]])/2 + (x^4*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}{5}+\frac {x^3}{4}+\frac {x}{2}+\frac {c_1}{2 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*}