ODE
\[ (a+x)^2 y''''(x)=1 \] ODE Classification
[[_high_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.166928 (sec), leaf count = 50
\[\left \{\left \{y(x)\to \frac {a x}{2}-\frac {1}{2} (a+x)^2 \log (a+x)+c_4 x^3+\frac {3 x^2}{4}+c_3 x^2+c_2 x+c_1\right \}\right \}\]
Maple ✓
cpu = 0.19 (sec), leaf count = 46
\[\left [y \left (x \right ) = \frac {3 x^{2}}{4}+\frac {3 a x}{2}+\frac {x^{2} \textit {\_C2}}{2}+\frac {\textit {\_C1} \,x^{3}}{6}-\frac {\ln \left (a +x \right ) \left (a +x \right )^{2}}{2}+\frac {a^{2}}{4}+\textit {\_C3} x +\textit {\_C4}\right ]\] 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))
Maple raw output
[y(x) = 3/4*x^2+3/2*a*x+1/2*x^2*_C2+1/6*_C1*x^3-1/2*ln(a+x)*(a+x)^2+1/4*a^2+_C3*x+_C4]