75.14.3 problem 329

Internal problem ID [16917]
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 : Tuesday, January 28, 2025 at 09:40:51 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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