73.7.37 problem 37

Internal problem ID [15116]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 37
Date solved : Thursday, March 13, 2025 at 05:40:48 AM
CAS classification : [_Bernoulli]

\begin{align*} y y^{\prime }-x y^{2}&=6 x \,{\mathrm e}^{4 x^{2}} \end{align*}

✓ Maple. Time used: 0.049 (sec). Leaf size: 43

ode:=y(x)*diff(y(x),x)-x*y(x)^2 = 6*x*exp(4*x^2); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {{\mathrm e}^{x^{2}} \left (2 \,{\mathrm e}^{3 x^{2}}+c_{1} \right )} \\ y &= -\sqrt {{\mathrm e}^{x^{2}} \left (2 \,{\mathrm e}^{3 x^{2}}+c_{1} \right )} \\ \end{align*}

✓ Mathematica. Time used: 1.991 (sec). Leaf size: 62

ode=y[x]*D[y[x],x]-x*y[x]^2==6*x*Exp[4*x^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -e^{\frac {x^2}{2}} \sqrt {2 e^{3 x^2}+c_1} \\ y(x)\to e^{\frac {x^2}{2}} \sqrt {2 e^{3 x^2}+c_1} \\ \end{align*}

✓ Sympy. Time used: 0.830 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x)**2 - 6*x*exp(4*x**2) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {\left (C_{1} + 2 e^{3 x^{2}}\right ) e^{x^{2}}}, \ y{\left (x \right )} = \sqrt {\left (C_{1} + 2 e^{3 x^{2}}\right ) e^{x^{2}}}\right ] \]