75.14.3 problem 329

Internal problem ID [16838]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 329
Date solved : Thursday, March 13, 2025 at 08:52:57 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime } \left (x +2\right )^{5}&=1 \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&={\frac {1}{12}}\\ y^{\prime }\left (-1\right )&=-{\frac {1}{4}} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 11

ode:=diff(diff(y(x),x),x)*(x+2)^5 = 1; 
ic:=y(-1) = 1/12, D(y)(-1) = -1/4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {1}{12 \left (x +2\right )^{3}} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 14

ode=D[y[x],{x,2}]*(x+2)^5==1; 
ic={y[-1]==1/12,Derivative[1][y][-1]==-1/4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{12 (x+2)^3} \]

✓ Sympy. Time used: 0.610 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 2)**5*Derivative(y(x), (x, 2)) - 1,0) 
ics = {y(-1): 1/12, Subs(Derivative(y(x), x), x, -1): -1/4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x + 2}{12 \left (x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16\right )} \]