ODE
\[ (a+x)^2 y''''(x)=1 \] ODE Classification
[[_high_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0197524 (sec), leaf count = 50
\[\left \{\left \{y(x)\to \frac {a x}{2}-\frac {1}{2} (a+x)^2 \log (a+x)+c_4 x^3+c_3 x^2+c_2 x+c_1+\frac {3 x^2}{4}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 48
\[ \left \{ y \left ( x \right ) =-{\frac {\ln \left ( a+x \right ) \left ( a+x \right ) ^{2}}{2}}+{\frac {{\it \_C1}\,{x}^{3}}{6}}+{\frac { \left ( 6\,{\it \_C2}+9 \right ) {x}^{2}}{12}}+{\frac { \left ( 18\,a+12\,{\it \_C3} \right ) x}{12}}+{\frac {{a}^{2}}{4}}+{\it \_C4} \right \} \] Mathematica raw input
DSolve[(a + x)^2*y''''[x] == 1,y[x],x]
Mathematica raw output
{{y[x] -> (a*x)/2 + (3*x^2)/4 + C[1] + x*C[2] + x^2*C[3] + x^3*C[4] - ((a + x)^2*Log[a + x])/2}}
Maple raw input
dsolve((a+x)^2*diff(diff(diff(diff(y(x),x),x),x),x) = 1, y(x),'implicit')
Maple raw output
y(x) = -1/2*ln(a+x)*(a+x)^2+1/6*_C1*x^3+1/12*(6*_C2+9)*x^2+1/12*(18*a+12*_C3)*x+1/4*a^2+_C4