Internal problem ID [15212]
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: 354.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {2 y^{\prime \prime }-3 y^{2}=0} \] With initial conditions \begin {align*} [y \left (-2\right ) = 1, y^{\prime }\left (-2\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 11
dsolve([2*diff(y(x),x$2)=3*y(x)^2,y(-2) = 1, D(y)(-2) = -1],y(x), singsol=all)
\[ y = \frac {4}{\left (x +4\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 12
DSolve[{2*y''[x]==3*y[x]^2,{y[-2]==1,y'[-2]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4}{(x+4)^2} \]