60.1.437 problem 439

Internal problem ID [10451]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 439
Date solved : Monday, January 27, 2025 at 07:45:48 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+3 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 33

dsolve(x^2*diff(y(x),x)^2+3*x*y(x)*diff(y(x),x)+3*y(x)^2 = 0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= x^{-\frac {3}{2}-\frac {i \sqrt {3}}{2}} c_{1} \\ y &= x^{-\frac {3}{2}+\frac {i \sqrt {3}}{2}} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 54

DSolve[3*y[x]^2 + 3*x*y[x]*D[y[x],x] + x^2*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x^{-\frac {3}{2}-\frac {i \sqrt {3}}{2}} \\ y(x)\to c_1 x^{\frac {1}{2} i \left (\sqrt {3}+3 i\right )} \\ y(x)\to 0 \\ \end{align*}