38.6.28 problem 28

Internal problem ID [8458]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 28
Date solved : Tuesday, September 30, 2025 at 05:37:24 PM
CAS classification : [_rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.132 (sec). Leaf size: 21

ode:=y(x)*diff(y(x),x)-x = 2*y(x)^2; 
ic:=[y(1) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sqrt {-2+410 \,{\mathrm e}^{-4+4 x}-8 x}}{4} \]

✓ Mathematica. Time used: 0.128 (sec). Leaf size: 40

ode=y[x]*D[y[x],x]-x==2*y[x]^2; 
ic={y[1]==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 x-2} \sqrt {2 e^4 \int _1^xe^{-4 K[1]} K[1]dK[1]+25} \end{align*}

✓ Sympy. Time used: 0.399 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - 2*y(x)**2 + y(x)*Derivative(y(x), x),0) 
ics = {y(1): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sqrt {- 8 x + \frac {410 e^{4 x}}{e^{4}} - 2}}{4} \]