15.5.21 problem 25

Internal problem ID [2957]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 25
Date solved : Monday, January 27, 2025 at 07:01:11 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

With initial conditions

\begin{align*} y \left (2\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 2.746 (sec). Leaf size: 40

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

\[ y = \operatorname {RootOf}\left (-3 \ln \left (x \right )+4 \ln \left (2\right )-4 \ln \left (5\right )+4 \ln \left (\frac {\textit {\_Z}^{2}+3 x}{x}\right )-2 \ln \left (\frac {\textit {\_Z}}{\sqrt {x}}\right )\right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

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