2.562   ODE No. 562

\[ a \sqrt [3]{y'(x)^3+1}+b x y'(x)-y(x)=0 \]

✓ Mathematica : cpu = 0.0853865 (sec), leaf count = 84

DSolve[-y[x] + b*x*Derivative[1][y][x] + a*(1 + Derivative[1][y][x]^3)^(1/3) == 0,y[x],x]
 

\[\text {Solve}\left [\left \{x=K[1]^{\frac {b}{1-b}} \left (\frac {a \int \frac {K[1]^{\frac {2 b-1}{b-1}}}{\left (K[1]^3+1\right )^{2/3}}dK[1]}{1-b}+c_1\right ),y(x)=a \sqrt [3]{K[1]^3+1}+b x K[1]\right \},\{K[1],y(x)\}\right ]\]

✓ Maple : cpu = 0.261 (sec), leaf count = 3288

dsolve(a*(diff(y(x),x)^3+1)^(1/3)+b*x*diff(y(x),x)-y(x)=0,y(x))
 

\[\text {Expression too large to display}\]