ODE
\[ y(x) \left (f(x) \left (\text {a1}+\text {b1} x^k-1\right )+\text {a2}+\text {b2} x^k+\text {c2} x^{2 k}+f'(x)+f(x)^2\right )+x y'(x) \left (\text {a1}+\text {b1} x^k+2 f(x)\right )+x^2 y''(x)=0 \] ODE Classification
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Book solution method
TO DO
Mathematica ✗
cpu = 1.7417 (sec), leaf count = 0 , could not solve
DSolve[y[x]*(a2 + b2*x^k + c2*x^(2*k) + (-1 + a1 + b1*x^k)*f[x] + f[x]^2 + Derivative[1][f][x]) + x*(a1 + b1*x^k + 2*f[x])*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 3.116 (sec), leaf count = 0 , result contains DESol or ODESolStruc
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Mathematica raw input
DSolve[y[x]*(a2 + b2*x^k + c2*x^(2*k) + (-1 + a1 + b1*x^k)*f[x] + f[x]^2 + f'[x]) + x*(a1 + b1*x^k + 2*f[x])*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[y[x]*(a2 + b2*x^k + c2*x^(2*k) + (-1 + a1 + b1*x^k)*f[x] + f[x]^2 + Derivative[1][f][x]) + x*(a1 + b1*x^k + 2*f[x])*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*(a1+b1*x^k+2*f(x))*diff(y(x),x)+(a2+b2*x^k+c2*x^(2*k)+(a1+b1*x^k-1)*f(x)+f(x)^2+diff(f(x),x))*y(x) = 0, y(x))
Maple raw output
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