60.1.15 problem 15

Internal problem ID [10029]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 15
Date solved : Monday, January 27, 2025 at 06:18:46 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Riccati]

\begin{align*} y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 34

DSolve[D[y[x],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*}