ODE
\[ \left (a x y'(x)-y(x)\right )^2+x y''(x)=b \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 60.1321 (sec), leaf count = 0 , could not solve
DSolve[(-y[x] + a*x*Derivative[1][y][x])^2 + x*Derivative[2][y][x] == b, y[x], x]
Maple ✗
cpu = 0.525 (sec), leaf count = 0 , could not solve
dsolve(x*diff(diff(y(x),x),x)+(a*x*diff(y(x),x)-y(x))^2 = b, y(x),'implicit')
Mathematica raw input
DSolve[(-y[x] + a*x*y'[x])^2 + x*y''[x] == b,y[x],x]
Mathematica raw output
DSolve[(-y[x] + a*x*Derivative[1][y][x])^2 + x*Derivative[2][y][x] == b, y[x], x]
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+(a*x*diff(y(x),x)-y(x))^2 = b, y(x),'implicit')
Maple raw output
dsolve(x*diff(diff(y(x),x),x)+(a*x*diff(y(x),x)-y(x))^2 = b, y(x),'implicit')