85.33.77 problem 78

Internal problem ID [22700]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 78
Date solved : Thursday, October 02, 2025 at 09:11:01 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} 2 x^{2}-y \,{\mathrm e}^{x}-{\mathrm e}^{x} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=2*x^2-y(x)*exp(x)-exp(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\frac {2 x^{3}}{3}+c_1 \right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 24

ode=(2*x^2-y[x]*Exp[x])-Exp[x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} e^{-x} \left (2 x^3+3 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 14

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

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