61.26.2 problem 2

Internal problem ID [12502]
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
Date solved : Tuesday, January 28, 2025 at 03:18:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\left (a x +b \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)-(a*x+b)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {AiryAi}\left (\frac {a x +b}{\left (-a \right )^{{2}/{3}}}\right )+c_{2} \operatorname {AiryBi}\left (\frac {a x +b}{\left (-a \right )^{{2}/{3}}}\right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]-(a*x+b)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {AiryAi}\left (\frac {b+a x}{a^{2/3}}\right )+c_2 \operatorname {AiryBi}\left (\frac {b+a x}{a^{2/3}}\right ) \]