84.16.6 problem 8.15

Internal problem ID [22186]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 8. Linear first-order differential equations. Supplementary problems
Problem number : 8.15
Date solved : Thursday, October 02, 2025 at 08:33:45 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+6 y x&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\pi \right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 17

ode:=diff(y(x),x)+6*x*y(x) = 0; 
ic:=[y(Pi) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 5 \,{\mathrm e}^{3 \left (\pi -x \right ) \left (\pi +x \right )} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

ode=D[y[x],x]+6*x*y[x]==0; 
ic={y[Pi]==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 5 e^{3 \pi ^2-3 x^2} \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x*y(x) + Derivative(y(x), x),0) 
ics = {y(pi): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 e^{3 \pi ^{2}} e^{- 3 x^{2}} \]