ODE
\[ \left (x^2+y(x)^2\right ) y''(x)=\left (y(x)^2+1\right ) \left (x y'(x)-y(x)\right ) \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 1.06297 (sec), leaf count = 0 , could not solve
DSolve[(x^2 + y[x]^2)*Derivative[2][y][x] == (1 + y[x]^2)*(-y[x] + x*Derivative[1][y][x]), y[x], x]
Maple ✗
cpu = 0.664 (sec), leaf count = 0 , could not solve
dsolve((x^2+y(x)^2)*diff(diff(y(x),x),x) = (1+y(x)^2)*(x*diff(y(x),x)-y(x)), y(x),'implicit')
Mathematica raw input
DSolve[(x^2 + y[x]^2)*y''[x] == (1 + y[x]^2)*(-y[x] + x*y'[x]),y[x],x]
Mathematica raw output
DSolve[(x^2 + y[x]^2)*Derivative[2][y][x] == (1 + y[x]^2)*(-y[x] + x*Derivative[1][y][x]), y[x], x]
Maple raw input
dsolve((x^2+y(x)^2)*diff(diff(y(x),x),x) = (1+y(x)^2)*(x*diff(y(x),x)-y(x)), y(x),'implicit')
Maple raw output
dsolve((x^2+y(x)^2)*diff(diff(y(x),x),x) = (1+y(x)^2)*(x*diff(y(x),x)-y(x)), y(x),'implicit')