60.3.10 problem 1010

Internal problem ID [11020]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1010
Date solved : Monday, January 27, 2025 at 10:42:00 PM
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: 0.031 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 42

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

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