4.34.18 \(x (\text {a1}+\text {b1} x) y'(x)+\text {a2} y(x)+x^3 y''(x)=0\)

ODE
\[ x (\text {a1}+\text {b1} x) y'(x)+\text {a2} y(x)+x^3 y''(x)=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.343581 (sec), leaf count = 62

\[\left \{\left \{y(x)\to (-1)^{\text {b1}+1} c_2 \text {a1}^{\text {b1}-1} \left (\frac {1}{x}\right )^{\text {b1}-1} \, _1F_1\left (-\frac {\text {a2}}{\text {a1}}+\text {b1}-1;\text {b1};\frac {\text {a1}}{x}\right )+c_1 \, _1F_1\left (-\frac {\text {a2}}{\text {a1}};2-\text {b1};\frac {\text {a1}}{x}\right )\right \}\right \}\]

Maple ✓
cpu = 0.569 (sec), leaf count = 63

\[\left [y \left (x \right ) = \textit {\_C1} \,x^{-\mathit {b1} +1} \KummerM \left (\frac {\mathit {a1} \left (-1+\mathit {b1} \right )-\mathit {a2}}{\mathit {a1}}, \mathit {b1} , \frac {\mathit {a1}}{x}\right )+\textit {\_C2} \,x^{-\mathit {b1} +1} \KummerU \left (\frac {\mathit {a1} \left (-1+\mathit {b1} \right )-\mathit {a2}}{\mathit {a1}}, \mathit {b1} , \frac {\mathit {a1}}{x}\right )\right ]\] Mathematica raw input

DSolve[a2*y[x] + x*(a1 + b1*x)*y'[x] + x^3*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]*Hypergeometric1F1[-(a2/a1), 2 - b1, a1/x] + (-1)^(1 + b1)*a1^(-1 
+ b1)*(x^(-1))^(-1 + b1)*C[2]*Hypergeometric1F1[-1 - a2/a1 + b1, b1, a1/x]}}

Maple raw input

dsolve(x^3*diff(diff(y(x),x),x)+x*(b1*x+a1)*diff(y(x),x)+a2*y(x) = 0, y(x))

Maple raw output

[y(x) = _C1*x^(-b1+1)*KummerM((a1*(-1+b1)-a2)/a1,b1,1/x*a1)+_C2*x^(-b1+1)*Kummer
U((a1*(-1+b1)-a2)/a1,b1,1/x*a1)]