Internal problem ID [3345]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 603.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {\left (1-x^{2}+y^{2}\right ) y^{\prime }-1-x^{2}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 28
dsolve((1-x^2+y(x)^2)*diff(y(x),x) = 1+x^2-y(x)^2,y(x), singsol=all)
\[ y \relax (x )^{2}+2 x y \relax (x )+x^{2}+2 \ln \left (-x +y \relax (x )\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.395 (sec). Leaf size: 25
DSolve[(1-x^2+y[x]^2)y'[x]==1+x^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^{\frac {1}{2} (y(x)+x)^2} (x-y(x))=c_1,y(x)\right ] \]