ODE
\[ 4 y(x) y'(x)^2 y''(x)=y'(x)^4+3 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.860343 (sec), leaf count = 157
\[\left \{\left \{y(x)\to -\frac {3}{8} e^{-4 c_1} \left (-\sqrt [3]{6} \left (-e^{4 c_1} \left (c_2+x\right )\right ){}^{4/3}-8\right )\right \},\left \{y(x)\to \frac {3}{8} e^{-4 c_1} \left (8+\sqrt [3]{6} \left (-i e^{4 c_1} \left (c_2+x\right )\right ){}^{4/3}\right )\right \},\left \{y(x)\to \frac {3}{8} e^{-4 c_1} \left (8+\sqrt [3]{6} \left (i e^{4 c_1} \left (c_2+x\right )\right ){}^{4/3}\right )\right \},\left \{y(x)\to \frac {3}{8} e^{-4 c_1} \left (\sqrt [3]{6} \left (e^{4 c_1} \left (c_2+x\right )\right ){}^{4/3}+8\right )\right \}\right \}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 91
\[ \left \{ -{\frac {4}{3\,{\it \_C1}} \left ( {\it \_C1}\,y \left ( x \right ) -3 \right ) ^{{\frac {3}{4}}}}-x-{\it \_C2}=0,{\frac {4}{3\,{\it \_C1}} \left ( {\it \_C1}\,y \left ( x \right ) -3 \right ) ^{{\frac {3}{4}}}}-x-{\it \_C2}=0,{\frac {-{\frac {4\,i}{3}}}{{\it \_C1}} \left ( {\it \_C1}\,y \left ( x \right ) -3 \right ) ^{{\frac {3}{4}}}}-x-{\it \_C2}=0,{\frac {{\frac {4\,i}{3}}}{{\it \_C1}} \left ( {\it \_C1}\,y \left ( x \right ) -3 \right ) ^{{\frac {3}{4}}}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[4*y[x]*y'[x]^2*y''[x] == 3 + y'[x]^4,y[x],x]
Mathematica raw output
{{y[x] -> (-3*(-8 - 6^(1/3)*(-(E^(4*C[1])*(x + C[2])))^(4/3)))/(8*E^(4*C[1]))}, {y[x] -> (3*(8 + 6^(1/3)*((-I)*E^(4*C[1])*(x + C[2]))^(4/3)))/(8*E^(4*C[1]))}, {y[x] -> (3*(8 + 6^(1/3)*(I*E^(4*C[1])*(x + C[2]))^(4/3)))/(8*E^(4*C[1]))}, {y[x] -> (3*(8 + 6^(1/3)*(E^(4*C[1])*(x + C[2]))^(4/3)))/(8*E^(4*C[1]))}}
Maple raw input
dsolve(4*y(x)*diff(y(x),x)^2*diff(diff(y(x),x),x) = diff(y(x),x)^4+3, y(x),'implicit')
Maple raw output
-4/3*(_C1*y(x)-3)^(3/4)/_C1-x-_C2 = 0, 4/3*(_C1*y(x)-3)^(3/4)/_C1-x-_C2 = 0, -4/3*I*(_C1*y(x)-3)^(3/4)/_C1-x-_C2 = 0, 4/3*I*(_C1*y(x)-3)^(3/4)/_C1-x-_C2 = 0