4.18.48 \(x^2 y'(x)^2=(x-y(x))^2\)

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 = 0.0051665 (sec), leaf count = 30

\[\left \{\left \{y(x)\to \frac {c_1}{x}+\frac {x}{2}\right \},\left \{y(x)\to x \left (c_1-\log (x)\right )\right \}\right \}\]

Maple
cpu = 0.012 (sec), leaf count = 24

\[ \left \{ y \relax (x ) = \left (-\ln \relax (x ) +{\it \_C1} \right ) x,y \relax (x ) ={\frac {x}{2}}+{\frac {{\it \_C1}}{x}} \right \} \] 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),'implicit')

Maple raw output

y(x) = (-ln(x)+_C1)*x, y(x) = 1/2*x+1/x*_C1