60.3.82 problem 1086

Internal problem ID [11092]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1086
Date solved : Monday, January 27, 2025 at 10:45:31 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 y^{\prime \prime }+9 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(4*diff(diff(y(x),x),x)+9*x*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 42

DSolve[9*x*y[x] + 4*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {AiryAi}\left (\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} x\right )+c_2 \operatorname {AiryBi}\left (\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} x\right ) \]