29.21.27 problem 603

Internal problem ID [5197]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 603
Date solved : Monday, January 27, 2025 at 10:20:35 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} \left (1-x^{2}+y^{2}\right ) y^{\prime }&=1+x^{2}-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.010 (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)
 

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

✓ Solution by Mathematica

Time used: 0.374 (sec). Leaf size: 25

DSolve[(1-x^2+y[x]^2)D[y[x],x]==1+x^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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