Internal problem ID [8590]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1010.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (a x +b \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(diff(diff(y(x),x),x)+(a*x+b)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \AiryAi \left (-\frac {a x +b}{a^{\frac {2}{3}}}\right )+c_{2} \AiryBi \left (-\frac {a x +b}{a^{\frac {2}{3}}}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 42
DSolve[(b + a*x)*y[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \text {Ai}\left (-\frac {b+a x}{(-a)^{2/3}}\right )+c_2 \text {Bi}\left (-\frac {b+a x}{(-a)^{2/3}}\right ) \\ \end{align*}