85.1.22 problem 12 (c)

Internal problem ID [22427]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 12 (c)
Date solved : Thursday, October 02, 2025 at 08:39:14 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=\sqrt {2 x +1} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ y \left (4\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x) = (2*x+1)^(1/2); 
ic:=[y(0) = 5, y(4) = -3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {4 \left (x +\frac {1}{2}\right )^{2} \sqrt {2 x +1}}{15}-\frac {181 x}{30}+\frac {74}{15} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 25

ode=D[y[x],{x,2}]==Sqrt[2*x+1]; 
ic={y[0]==5,y[4]==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{30} \left (2 (2 x+1)^{5/2}-181 x+148\right ) \end{align*}

✓ Sympy. Time used: 0.348 (sec). Leaf size: 56

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(2*x + 1) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 5, y(4): -3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {2 x^{2} \sqrt {2 x + 1}}{5} + x \left (\frac {\left (2 x + 1\right )^{\frac {3}{2}}}{3} - \frac {\sqrt {2 x + 1}}{15} - \frac {181}{30}\right ) + \frac {\sqrt {2 x + 1}}{15} + \frac {74}{15} \]