Internal problem ID [1917]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +y}{x -y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.153 (sec). Leaf size: 23
dsolve([diff(y(x),x)=(x+y(x))/(x-y(x)),y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \left (\RootOf \left (2 \textit {\_Z} -\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )-2 \ln \relax (x )\right )\right ) x}{\cos \left (\RootOf \left (2 \textit {\_Z} -\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )-2 \ln \relax (x )\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 33
DSolve[{y'[x]==(x+y[x])/(x-y[x]),y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )-\text {ArcTan}\left (\frac {y(x)}{x}\right )=-\log (x),y(x)\right ] \]