ODE
\[ \left (x^2+y(x)^2\right ) y''(x)=2 \left (y(x)^2+1\right ) \left (x y'(x)-y(x)\right ) \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 0.998599 (sec), leaf count = 0 , could not solve
DSolve[(x^2 + y[x]^2)*Derivative[2][y][x] == 2*(1 + y[x]^2)*(-y[x] + x*Derivative[1][y][x]), y[x], x]
Maple ✗
cpu = 0.971 (sec), leaf count = 0 , could not solve
dsolve((x^2+y(x)^2)*diff(diff(y(x),x),x) = 2*(1+y(x)^2)*(x*diff(y(x),x)-y(x)), y(x))
Mathematica raw input
DSolve[(x^2 + y[x]^2)*y''[x] == 2*(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] == 2*(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) = 2*(1+y(x)^2)*(x*diff(y(x),x)-y(x)), y(x))
Maple raw output
dsolve((x^2+y(x)^2)*diff(diff(y(x),x),x) = 2*(1+y(x)^2)*(x*diff(y(x),x)-y(x)), y(x))