ODE
\[ 4 x^4 y'''(x)-4 x^3 y''(x)+4 x^2 y'(x)=1 \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0235126 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \frac {1}{4} \left (2 c_1-c_2\right ) x^2+\frac {1}{2} c_2 x^2 \log (x)+c_3-\frac {1}{36 x}\right \}\right \}\]
Maple ✓
cpu = 0.029 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac {18\,{x}^{3}{\it \_C1}\,\ln \left ( x \right ) -1+ \left ( -9\,{\it \_C1}+18\,{\it \_C2} \right ) {x}^{3}+36\,{\it \_C3}\,x}{36\,x}} \right \} \] Mathematica raw input
DSolve[4*x^2*y'[x] - 4*x^3*y''[x] + 4*x^4*y'''[x] == 1,y[x],x]
Mathematica raw output
{{y[x] -> -1/(36*x) + (x^2*(2*C[1] - C[2]))/4 + C[3] + (x^2*C[2]*Log[x])/2}}
Maple raw input
dsolve(4*x^4*diff(diff(diff(y(x),x),x),x)-4*x^3*diff(diff(y(x),x),x)+4*x^2*diff(y(x),x) = 1, y(x),'implicit')
Maple raw output
y(x) = 1/36*(18*x^3*_C1*ln(x)-1+(-9*_C1+18*_C2)*x^3+36*_C3*x)/x