84.26.5 problem 15.10

Internal problem ID [22272]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 15. Variation of parameteres. Supplementary problems
Problem number : 15.10
Date solved : Thursday, October 02, 2025 at 08:36:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y x&=x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)+2*x*y(x) = x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 63

ode=D[y[x],{x,2}]+2*x*y[x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2} \pi \operatorname {AiryAiPrime}\left (\sqrt [3]{-2} x\right ) \operatorname {AiryBi}\left (\sqrt [3]{-2} x\right )+c_2 \operatorname {AiryBi}\left (\sqrt [3]{-2} x\right )+\operatorname {AiryAi}\left (\sqrt [3]{-2} x\right ) \left (\frac {1}{2} \pi \operatorname {AiryBiPrime}\left (\sqrt [3]{-2} x\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x) - x + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} Ai\left (- \sqrt [3]{2} x\right ) + C_{2} Bi\left (- \sqrt [3]{2} x\right ) \]