2.1676   ODE No. 1676

\[ a \left (x y'(x)-y(x)\right )^2-b x^2+x^2 y''(x)=0 \]

✓ Mathematica : cpu = 0.389642 (sec), leaf count = 134

DSolve[-(b*x^2) + a*(-y[x] + x*Derivative[1][y][x])^2 + x^2*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to x \left (\int _1^x\frac {i \sqrt {a} \sqrt {b} Y_1\left (-i \sqrt {a} \sqrt {b} K[1]\right )-i \sqrt {a} \sqrt {b} J_1\left (i \sqrt {a} \sqrt {b} K[1]\right ) c_1}{a \left (Y_0\left (-i \sqrt {a} \sqrt {b} K[1]\right )+J_0\left (i \sqrt {a} \sqrt {b} K[1]\right ) c_1\right ) K[1]}dK[1]+c_2\right )\right \}\right \}\]

✓ Maple : cpu = 0.224 (sec), leaf count = 72

dsolve(x^2*diff(diff(y(x),x),x)+a*(x*diff(y(x),x)-y(x))^2-b*x^2=0,y(x))
 

\[y \left (x \right ) = \left (\int -\frac {\sqrt {-a b}\, \left (c_{1} \operatorname {BesselY}\left (1, \sqrt {-a b}\, x \right )+\operatorname {BesselJ}\left (1, \sqrt {-a b}\, x \right )\right )}{x a \left (c_{1} \operatorname {BesselY}\left (0, \sqrt {-a b}\, x \right )+\operatorname {BesselJ}\left (0, \sqrt {-a b}\, x \right )\right )}d x +c_{2} \right ) x\]