1.15 problem 15

Internal problem ID [7596]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 15.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Riccati]

Solve \begin {gather*} \boxed {y^{\prime }+y^{2}-2 y x^{2}+x^{4}-2 x -1=0} \end {gather*}

Solution by Maple

Time used: 0.078 (sec). Leaf size: 37

dsolve(diff(y(x),x) + y(x)^2 - 2*x^2*y(x) + x^4 -2*x-1=0,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x^{2} {\mathrm e}^{2 x} c_{1}-x^{2}+{\mathrm e}^{2 x} c_{1}+1}{{\mathrm e}^{2 x} c_{1}-1} \]

Solution by Mathematica

Time used: 0.264 (sec). Leaf size: 34

DSolve[y'[x] + y[x]^2 - 2*x^2*y[x] + x^4 -2*x-1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^2-\frac {2}{1+2 c_1 e^{2 x}}+1 \\ y(x)\to x^2+1 \\ \end{align*}