84.16.11 problem 8.20

Internal problem ID [22191]
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 : 8.20
Date solved : Thursday, October 02, 2025 at 08:33:51 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=diff(y(x),x)+x*y(x) = 6*x*y(x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ -6-{\mathrm e}^{-\frac {x^{2}}{4}} c_1 +\sqrt {y} = 0 \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 47

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

\begin{align*} y(x)&\to e^{-\frac {x^2}{2}} \left (6 e^{\frac {x^2}{4}}+e^{\frac {c_1}{2}}\right ){}^2\\ y(x)&\to 0\\ y(x)&\to 36 \end{align*}

✓ Sympy. Time used: 0.342 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = 12 e^{\frac {C_{1}}{2} - \frac {x^{2}}{4}} + e^{C_{1} - \frac {x^{2}}{2}} + 36 \]