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