4.18.45 \(x^2 y'(x)^2=a^2\)

ODE
\[ x^2 y'(x)^2=a^2 \] ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Mathematica
cpu = 0.00319314 (sec), leaf count = 24

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

Maple
cpu = 0.007 (sec), leaf count = 20

\[ \left \{ y \relax (x ) =-a\ln \relax (x ) +{\it \_C1},y \relax (x ) =a\ln \relax (x ) +{\it \_C1} \right \} \] Mathematica raw input

DSolve[x^2*y'[x]^2 == a^2,y[x],x]

Mathematica raw output

{{y[x] -> C[1] - a*Log[x]}, {y[x] -> C[1] + a*Log[x]}}

Maple raw input

dsolve(x^2*diff(y(x),x)^2 = a^2, y(x),'implicit')

Maple raw output

y(x) = a*ln(x)+_C1, y(x) = -a*ln(x)+_C1