Internal problem ID [15187]
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 ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 329.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime } \left (x +2\right )^{5}=1} \] With initial conditions \begin {align*} \left [y \left (-1\right ) = {\frac {1}{12}}, y^{\prime }\left (-1\right ) = -{\frac {1}{4}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (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: 0.013 (sec). Leaf size: 14
DSolve[{y''[x]*(x+2)^5==1,{y[-1]==1/12,y'[-1]==-1/4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12 (x+2)^3} \]