ODE
\[ a x+2 y'(x)=\sqrt {a^2 x^2-4 b x^2-4 c y(x)} \] ODE Classification
[[_homogeneous, `class G`]]
Book solution method
Homogeneous equation, isobaric equation
Mathematica ✗
cpu = 599.993 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.198 (sec), leaf count = 198
\[ \left \{ \int _{{\it \_b}}^{x}\!{1 \left ( -a{\it \_a}+\sqrt {-4\,cy \left ( x \right ) + \left ( {a}^{2}-4\,b \right ) {{\it \_a}}^{2}} \right ) \left ( a{{\it \_a}}^{2}-{\it \_a}\,\sqrt {-4\,cy \left ( x \right ) + \left ( {a}^{2}-4\,b \right ) {{\it \_a}}^{2}}+4\,y \left ( x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!2\, \left ( -a{x}^{2}+x\sqrt { \left ( {a}^{2}-4\,b \right ) {x}^{2}-4\,{\it \_f}\,c}-4\,{\it \_f} \right ) ^{-1}-\int _{{\it \_b}}^{x}\!{1 \left ( -8\,{\frac {{\it \_f}\,c}{\sqrt { \left ( {a}^{2}-4\,b \right ) {{\it \_a}}^{2}-4\,{\it \_f}\,c}}}+4\,a{\it \_a}-4\,\sqrt { \left ( {a}^{2}-4\,b \right ) {{\it \_a}}^{2}-4\,{\it \_f}\,c} \right ) \left ( a{{\it \_a}}^{2}-{\it \_a}\,\sqrt { \left ( {a}^{2}-4\,b \right ) {{\it \_a}}^{2}-4\,{\it \_f}\,c}+4\,{\it \_f} \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[a*x + 2*y'[x] == Sqrt[a^2*x^2 - 4*b*x^2 - 4*c*y[x]],y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(2*diff(y(x),x)+a*x = (a^2*x^2-4*b*x^2-4*c*y(x))^(1/2), y(x),'implicit')
Maple raw output
Int((-a*_a+(-4*c*y(x)+(a^2-4*b)*_a^2)^(1/2))/(a*_a^2-_a*(-4*c*y(x)+(a^2-4*b)*_a^2)^(1/2)+4*y(x)),_a = _b .. x)+Intat(2/(-a*x^2+x*((a^2-4*b)*x^2-4*_f*c)^(1/2)-4*_f)-Int((-8*c*_f/((a^2-4*b)*_a^2-4*_f*c)^(1/2)+4*a*_a-4*((a^2-4*b)*_a^2-4*_f*c)^(1/2))/(a*_a^2-_a*((a^2-4*b)*_a^2-4*_f*c)^(1/2)+4*_f)^2,_a = _b .. x),_f = y(x))+_C1 = 0