Internal problem ID [10177]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary.
Page 29
Problem number: Ex 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (y^{2}+x^{2}\right ) \left (x +y^{\prime } y\right )-\left (x^{2}+y^{2}+x \right ) \left (y^{\prime } x -y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 59
dsolve((x^2+y(x)^2)*(x+y(x)*diff(y(x),x))=(x^2+y(x)^2+x)*(x*diff(y(x),x)-y(x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{\tan \left (\RootOf \left (-2 \textit {\_Z} +2 \ln \left (\frac {x \left (2 x \left (\tan ^{2}\left (\textit {\_Z} \right )\right )+\tan ^{2}\left (\textit {\_Z} \right )+2 x +\tan \left (\textit {\_Z} \right )\right )}{\tan \left (\textit {\_Z} \right )^{2}}\right )-\ln \left (\frac {x^{2} \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right )}{\tan \left (\textit {\_Z} \right )^{2}}\right )+c_{1}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.362 (sec). Leaf size: 53
DSolve[(x^2+y[x]^2)*(x+y[x]*y'[x])==(x^2+y[x]^2+x)*(x*y'[x]-y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \text {ArcTan}\left (\frac {x}{y(x)}\right )-\frac {1}{4} \log \left (x^2+y(x)^2\right )+\frac {1}{2} \log \left (2 x^2+2 y(x)^2-y(x)+x\right )=c_1,y(x)\right ] \]