Internal problem ID [10836]
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]]
\[ \boxed {y^{\prime \prime }-\left (a x +b \right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)-(a*x+b)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {AiryAi}\left (\frac {a x +b}{\left (-a \right )^{\frac {2}{3}}}\right )+c_{2} \operatorname {AiryBi}\left (\frac {a x +b}{\left (-a \right )^{\frac {2}{3}}}\right ) \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 36
DSolve[y''[x]-(a*x+b)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {AiryAi}\left (\frac {b+a x}{a^{2/3}}\right )+c_2 \operatorname {AiryBi}\left (\frac {b+a x}{a^{2/3}}\right ) \]