Internal problem ID [3853]
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]
\[ \boxed {\left (1-x^{2}+y^{2}\right ) y^{\prime }+y^{2}=x^{2}+1} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right )^{2}+2 y \left (x \right ) x +x^{2}+2 \ln \left (y \left (x \right )-x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.349 (sec). Leaf size: 25
DSolve[(1-x^2+y[x]^2)y'[x]==1+x^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^{\frac {1}{2} (y(x)+x)^2} (x-y(x))=c_1,y(x)\right ] \]