15.8.47 problem 50

Internal problem ID [3050]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 50
Date solved : Monday, January 27, 2025 at 07:11:59 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 5.935 (sec). Leaf size: 21

dsolve([(3*x*y(x))+(3*x^2+y(x)^2)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
 

\[ y = \sqrt {-3 x^{2}+\sqrt {9 x^{4}+1}} \]

✓ Solution by Mathematica

Time used: 9.022 (sec). Leaf size: 26

DSolve[{(3*x*y[x])+(3*x^2+y[x]^2)*D[y[x],x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {\sqrt {9 x^4+1}-3 x^2} \]