2.1670   ODE No. 1670

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

✓ Mathematica : cpu = 7.37579 (sec), leaf count = 51

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

\[\left \{\left \{y(x)\to x \left (\int _1^x\frac {\sqrt {-\frac {b}{a}} \tan \left (c_1-a \sqrt {-\frac {b}{a}} K[2]\right )}{K[2]^2}dK[2]+c_2\right )\right \}\right \}\]

✓ Maple : cpu = 0.632 (sec), leaf count = 35

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

\[y \left (x \right ) = \left (\int \frac {i \tan \left (-i x \sqrt {a}\, \sqrt {b}+c_{1} \right ) \sqrt {b}}{\sqrt {a}\, x^{2}}d x +c_{2} \right ) x\]