85.27.1 problem 1

Internal problem ID [22593]
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 60
Problem number : 1
Date solved : Thursday, October 02, 2025 at 08:54:48 PM
CAS classification : [[_2nd_order, _quadrature]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=10 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x) = 2*x; 
ic:=[y(0) = 0, D(y)(0) = 10]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {1}{3} x^{3}+10 x \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 15

ode=D[y[x],{x,2}]==2*x; 
ic={y[0]==0,Derivative[1][y][0] ==10}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} x \left (x^2+30\right ) \end{align*}

✓ Sympy. Time used: 0.036 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 10} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{3}}{3} + 10 x \]