Internal problem ID [10083]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2 Equations Containing Power
Functions. page 213
Problem number: 2.
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: 0.011 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)-(a*x+b)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \AiryAi \left (\frac {x a +b}{\left (-a \right )^{\frac {2}{3}}}\right )+c_{2} \AiryBi \left (\frac {x a +b}{\left (-a \right )^{\frac {2}{3}}}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 36
DSolve[y''[x]-(a*x+b)*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*}