85.33.35 problem 35

Internal problem ID [22658]
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 : 35
Date solved : Thursday, October 02, 2025 at 09:03:03 PM
CAS classification : [[_2nd_order, _missing_y]]

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

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

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

\[ y = {\mathrm e}^{x} c_1 -x^{2}-2 x +c_2 \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to -x^2-2 x+c_1 e^x+c_2 \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 15

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

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