ODE
\[ 2 y(x) y''(x)=y(x)^2 (a x+b y(x))+y'(x)^2 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 1.24628 (sec), leaf count = 0 , could not solve
DSolve[2*y[x]*Derivative[2][y][x] == y[x]^2*(a*x + b*y[x]) + Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 0.198 (sec), leaf count = 0 , could not solve
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+(a*x+b*y(x))*y(x)^2, y(x),'implicit')
Mathematica raw input
DSolve[2*y[x]*y''[x] == y[x]^2*(a*x + b*y[x]) + y'[x]^2,y[x],x]
Mathematica raw output
DSolve[2*y[x]*Derivative[2][y][x] == y[x]^2*(a*x + b*y[x]) + Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+(a*x+b*y(x))*y(x)^2, y(x),'implicit')
Maple raw output
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+(a*x+b*y(x))*y(x)^2, y(x),'implicit')