60.1.29 problem 29

Internal problem ID [10043]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 29
Date solved : Monday, January 27, 2025 at 06:19:20 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \frac {3}{-1+3 \,{\mathrm e}^{-\frac {3 x^{2}}{2}} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.205 (sec). Leaf size: 46

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] (K[1]+3)}dK[1]\&\right ]\left [\frac {x^2}{2}+c_1\right ] \\ y(x)\to -3 \\ y(x)\to 0 \\ \end{align*}