75.14.28 problem 354

Internal problem ID [16942]
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 : 354
Date solved : Tuesday, January 28, 2025 at 09:42:55 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} 2 y^{\prime \prime }&=3 y^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.028 (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: 0.043 (sec). Leaf size: 12

DSolve[{2*D[y[x],{x,2}]==3*y[x]^2,{y[-2]==1,Derivative[1][y][-2]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4}{(x+4)^2} \]