ODE
\[ \left (a^2 x^2-y(x)^2\right ) y'(x)^2+\left (a^2-1\right ) x^2-2 x y(x) y'(x)=0 \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✗
cpu = 601.706 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.652 (sec), leaf count = 160
\[ \left \{ -{a}^{2}{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}=0,\ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( -{{\it \_a}}^{2}+{a}^{2}-1 \right ) } \left ( -{\it \_a}\,{a}^{2}+{{\it \_a}}^{3}+{\it \_a}-\sqrt {{{\it \_a}}^{2}{a}^{2}-{a}^{4}+{a}^{2}} \right ) }{d{\it \_a}}-{\it \_C1}=0,\ln \left ( x \right ) +\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( -{{\it \_a}}^{2}+{a}^{2}-1 \right ) } \left ( {\it \_a}\,{a}^{2}-{{\it \_a}}^{3}-{\it \_a}-\sqrt {{{\it \_a}}^{2}{a}^{2}-{a}^{4}+{a}^{2}} \right ) }{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[(-1 + a^2)*x^2 - 2*x*y[x]*y'[x] + (a^2*x^2 - y[x]^2)*y'[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve((a^2*x^2-y(x)^2)*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+(a^2-1)*x^2 = 0, y(x),'implicit')
Maple raw output
-a^2*x^2+y(x)^2+x^2 = 0, ln(x)-Intat((-_a*a^2+_a^3+_a-(_a^2*a^2-a^4+a^2)^(1/2))/(_a^2+1)/(-_a^2+a^2-1),_a = y(x)/x)-_C1 = 0, ln(x)+Intat((_a*a^2-_a^3-_a-(_a^2*a^2-a^4+a^2)^(1/2))/(_a^2+1)/(-_a^2+a^2-1),_a = y(x)/x)-_C1 = 0