ODE
\[ y''(x) \left (a \left (x y'(x)-y(x)\right )+y'(x)^2\right )=b \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.169849 (sec), leaf count = 0 , could not solve
DSolve[(Derivative[1][y][x]^2 + a*(-y[x] + x*Derivative[1][y][x]))*Derivative[2][y][x] == b, y[x], x]
Maple ✓
cpu = 0.358 (sec), leaf count = 285
\[ \left \{ x-\int ^{y \left ( x \right ) +{\frac {a{x}^{2}}{4}}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt { \left ( {\it \_f}\,a-\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}} \right ) \left ( {{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1} \right ) }}{d{\it \_f}}-{\it \_C2}=0,x+\int ^{y \left ( x \right ) +{\frac {a{x}^{2}}{4}}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt { \left ( {\it \_f}\,a-\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}} \right ) \left ( {{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1} \right ) }}{d{\it \_f}}-{\it \_C2}=0,x-\int ^{y \left ( x \right ) +{\frac {a{x}^{2}}{4}}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt { \left ( {\it \_f}\,a+\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}} \right ) \left ( {{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1} \right ) }}{d{\it \_f}}-{\it \_C2}=0,x+\int ^{y \left ( x \right ) +{\frac {a{x}^{2}}{4}}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt { \left ( {\it \_f}\,a+\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}} \right ) \left ( {{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1} \right ) }}{d{\it \_f}}-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[(y'[x]^2 + a*(-y[x] + x*y'[x]))*y''[x] == b,y[x],x]
Mathematica raw output
DSolve[(Derivative[1][y][x]^2 + a*(-y[x] + x*Derivative[1][y][x]))*Derivative[2][y][x] == b, y[x], x]
Maple raw input
dsolve((diff(y(x),x)^2+a*(x*diff(y(x),x)-y(x)))*diff(diff(y(x),x),x) = b, y(x),'implicit')
Maple raw output
x-Intat(1/(_f^2*a^2-4*_f*b+2*_C1)*((_f*a+(4*_f*b-2*_C1)^(1/2))*(_f^2*a^2-4*_f*b+2*_C1))^(1/2),_f = y(x)+1/4*a*x^2)-_C2 = 0, x-Intat(1/(_f^2*a^2-4*_f*b+2*_C1)*((_f*a-(4*_f*b-2*_C1)^(1/2))*(_f^2*a^2-4*_f*b+2*_C1))^(1/2),_f = y(x)+1/4*a*x^2)-_C2 = 0, x+Intat(1/(_f^2*a^2-4*_f*b+2*_C1)*((_f*a+(4*_f*b-2*_C1)^(1/2))*(_f^2*a^2-4*_f*b+2*_C1))^(1/2),_f = y(x)+1/4*a*x^2)-_C2 = 0, x+Intat(1/(_f^2*a^2-4*_f*b+2*_C1)*((_f*a-(4*_f*b-2*_C1)^(1/2))*(_f^2*a^2-4*_f*b+2*_C1))^(1/2),_f = y(x)+1/4*a*x^2)-_C2 = 0