38.4.36 problem 17

Internal problem ID [8335]
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 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 05:29:08 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

\[ y = \frac {x^{2}}{2}-\frac {x}{2}+\frac {1}{4}+{\mathrm e}^{-2 x} c_1 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to e^{-2 x} \left (\int _1^xe^{2 K[1]} K[1]^2dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 20

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

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