4.46.15 \(\text {A1} x^3 y'''(x)+x^4 y''''(x)+\text {A2} x^2 y''(x)+\text {A3} x y'(x)+\text {A4} y(x)=0\)

ODE
\[ \text {A1} x^3 y'''(x)+x^4 y''''(x)+\text {A2} x^2 y''(x)+\text {A3} x y'(x)+\text {A4} y(x)=0 \] ODE Classification

[[_high_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0140151 (sec), leaf count = 186

\[\left \{\left \{y(x)\to c_1 x^{\text {Root}\left [\text {$\#$1}^4+\text {$\#$1}^3 (\text {A1}-6)+\text {$\#$1}^2 (-3 \text {A1}+\text {A2}+11)+\text {$\#$1} (2 \text {A1}-\text {A2}+\text {A3}-6)+\text {A4}\& ,1\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^4+\text {$\#$1}^3 (\text {A1}-6)+\text {$\#$1}^2 (-3 \text {A1}+\text {A2}+11)+\text {$\#$1} (2 \text {A1}-\text {A2}+\text {A3}-6)+\text {A4}\& ,2\right ]}+c_3 x^{\text {Root}\left [\text {$\#$1}^4+\text {$\#$1}^3 (\text {A1}-6)+\text {$\#$1}^2 (-3 \text {A1}+\text {A2}+11)+\text {$\#$1} (2 \text {A1}-\text {A2}+\text {A3}-6)+\text {A4}\& ,3\right ]}+c_4 x^{\text {Root}\left [\text {$\#$1}^4+\text {$\#$1}^3 (\text {A1}-6)+\text {$\#$1}^2 (-3 \text {A1}+\text {A2}+11)+\text {$\#$1} (2 \text {A1}-\text {A2}+\text {A3}-6)+\text {A4}\& ,4\right ]}\right \}\right \}\]

Maple ✓
cpu = 0.018 (sec), leaf count = 51

\[ \left \{ y \left ( x \right ) =\sum _{{\it \_a}=1}^{4}{x}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+ \left ( {\it A1}-6 \right ) {{\it \_Z}}^{3}+ \left ( {\it A2}-3\,{\it A1}+11 \right ) {{\it \_Z}}^{2}+ \left ( {\it A3}-{\it A2}+2\,{\it A1}-6 \right ) {\it \_Z}+{\it A4},{\it index}={\it \_a} \right ) }{\it \_C}_{{{\it \_a}}} \right \} \] Mathematica raw input

DSolve[A4*y[x] + A3*x*y'[x] + A2*x^2*y''[x] + A1*x^3*y'''[x] + x^4*y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x^Root[A4 + (-6 + 2*A1 - A2 + A3)*#1 + (11 - 3*A1 + A2)*#1^2 + (-6 + A
1)*#1^3 + #1^4 & , 1]*C[1] + x^Root[A4 + (-6 + 2*A1 - A2 + A3)*#1 + (11 - 3*A1 +
 A2)*#1^2 + (-6 + A1)*#1^3 + #1^4 & , 2]*C[2] + x^Root[A4 + (-6 + 2*A1 - A2 + A3
)*#1 + (11 - 3*A1 + A2)*#1^2 + (-6 + A1)*#1^3 + #1^4 & , 3]*C[3] + x^Root[A4 + (
-6 + 2*A1 - A2 + A3)*#1 + (11 - 3*A1 + A2)*#1^2 + (-6 + A1)*#1^3 + #1^4 & , 4]*C
[4]}}

Maple raw input

dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+A1*x^3*diff(diff(diff(y(x),x),x),x)+A2*x^2*diff(diff(y(x),x),x)+A3*x*diff(y(x),x)+A4*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = Sum(x^RootOf(_Z^4+(A1-6)*_Z^3+(A2-3*A1+11)*_Z^2+(A3-A2+2*A1-6)*_Z+A4,inde
x = _a)*_C[_a],_a = 1 .. 4)