Internal problem ID [8527]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 947.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 \cos \relax (x ) x^{2}+2 x^{3} \sin \relax (x )-2 \sin \relax (x ) x +2 x +2 y^{2} x^{2}-4 y \sin \relax (x ) x +4 y \cos \relax (x ) x^{2}+4 y x +3-\cos \left (2 x \right )-2 \sin \left (2 x \right ) x -4 \sin \relax (x )+x^{2} \cos \left (2 x \right )+x^{2}+4 \cos \relax (x ) x}{2 x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x) = 1/2*(2*x^2*cos(x)+2*sin(x)*x^3-2*x*sin(x)+2*x+2*x^2*y(x)^2-4*y(x)*sin(x)*x+4*y(x)*cos(x)*x^2+4*x*y(x)+3-cos(2*x)-2*sin(2*x)*x-4*sin(x)+x^2*cos(2*x)+x^2+4*cos(x)*x)/x^3,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (\frac {2 \cos \relax (x )}{x}-\frac {2 \sin \relax (x )}{x^{2}}+\frac {2}{x^{2}}\right ) x}{2}+\frac {1}{c_{1}-\ln \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.606 (sec). Leaf size: 45
DSolve[y'[x] == (3/2 + x + x^2/2 + 2*x*Cos[x] + x^2*Cos[x] - Cos[2*x]/2 + (x^2*Cos[2*x])/2 - 2*Sin[x] - x*Sin[x] + x^3*Sin[x] - x*Sin[2*x] + 2*x*y[x] + 2*x^2*Cos[x]*y[x] - 2*x*Sin[x]*y[x] + x^2*y[x]^2)/x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sin (x)-x \cos (x)-1}{x}+\frac {1}{-\log (x)+c_1} \\ y(x)\to \frac {\sin (x)-x \cos (x)-1}{x} \\ \end{align*}