75.14.27 problem 353

Internal problem ID [16941]
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 : 353
Date solved : Tuesday, January 28, 2025 at 09:42:53 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 11

dsolve([3*diff(y(x),x)*diff(y(x),x$2)=2*y(x),y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = \frac {\left (x +3\right )^{3}}{27} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{3*D[y[x],x]*D[y[x],{x,2}]==2*y[x],{y[0]==1,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

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