83.8.17 problem 18

Internal problem ID [19143]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 01:05:21 PM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 21

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

\[ x +\frac {\ln \left (x^{2}+y \left (x \right )^{2}\right )}{2}-2 y \left (x \right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.201 (sec). Leaf size: 27

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

\[ \text {Solve}\left [-\frac {1}{2} \log \left (x^2+y(x)^2\right )+2 y(x)-x=c_1,y(x)\right ] \]