60.1.449 problem 452

Internal problem ID [10463]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 452
Date solved : Monday, January 27, 2025 at 07:46:40 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 49

DSolve[1 + 2*y[x]^2 + (2 + x^2 + 2*x*y[x] + y[x]^2)*D[y[x],x] + (1 + 2*x^2)*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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