60.1.283 problem 284

Internal problem ID [10297]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 284
Date solved : Monday, January 27, 2025 at 06:51:05 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 32

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

\[ y = \frac {{\mathrm e}^{-c_{1}} \sqrt {\frac {{\mathrm e}^{2 c_{1}} x^{2}}{\operatorname {LambertW}\left (\frac {{\mathrm e}^{2 c_{1}} x^{2}}{4}\right )}}}{2} \]

✓ Solution by Mathematica

Time used: 9.737 (sec). Leaf size: 64

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

\begin{align*} y(x)\to -\frac {x}{2 \sqrt {W\left (\frac {1}{4} e^{-\frac {c_1}{2}} x^2\right )}} \\ y(x)\to \frac {x}{2 \sqrt {W\left (\frac {1}{4} e^{-\frac {c_1}{2}} x^2\right )}} \\ y(x)\to 0 \\ \end{align*}