60.1.439 problem 441

Internal problem ID [10453]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 441
Date solved : Monday, January 27, 2025 at 07:45:53 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 y \left (y+2\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 83

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

\begin{align*} y &= -2 \\ y &= \frac {-2 \sqrt {2}\, \sqrt {c_{1} x^{2}}+x^{2}}{c_{1}} \\ y &= \frac {2 \sqrt {2}\, \sqrt {c_{1} x^{2}}+x^{2}}{c_{1}} \\ y &= \frac {\left (-2 c_{1} \sqrt {2}+x \right ) x}{c_{1}^{2}} \\ y &= \frac {x \left (2 c_{1} \sqrt {2}+x \right )}{c_{1}^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 69

DSolve[4*y[x]*(2 + y[x]) - 4*x*(2 + y[x])*D[y[x],x] + x^2*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-c_1} x \left (x-2 \sqrt {2} e^{\frac {c_1}{2}}\right ) \\ y(x)\to e^{c_1} x^2-2 \sqrt {2} e^{\frac {c_1}{2}} x \\ y(x)\to -2 \\ y(x)\to 0 \\ \end{align*}