ODE
\[ x^2 y'(x)^2=(x-y(x))^2 \] ODE Classification
[_linear]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.181687 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {x}{2}+\frac {c_1}{x}\right \},\{y(x)\to x (-\log (x)+c_1)\}\right \}\]
Maple ✓
cpu = 0.043 (sec), leaf count = 24
\[\left [y \left (x \right ) = \left (-\ln \left (x \right )+\textit {\_C1} \right ) x, y \left (x \right ) = \frac {x}{2}+\frac {\textit {\_C1}}{x}\right ]\] Mathematica raw input
DSolve[x^2*y'[x]^2 == (x - y[x])^2,y[x],x]
Mathematica raw output
{{y[x] -> x/2 + C[1]/x}, {y[x] -> x*(C[1] - Log[x])}}
Maple raw input
dsolve(x^2*diff(y(x),x)^2 = (x-y(x))^2, y(x))
Maple raw output
[y(x) = (-ln(x)+_C1)*x, y(x) = 1/2*x+1/x*_C1]