60.2.330 problem 907

Internal problem ID [10917]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 907
Date solved : Monday, January 27, 2025 at 10:24:01 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.425 (sec). Leaf size: 32

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

\begin{align*} y(x)\to x+x (-\cos (x))+\frac {1}{-\log (x)+c_1} \\ y(x)\to x-x \cos (x) \\ \end{align*}