75.14.37 problem 363

Internal problem ID [16951]
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 : 363
Date solved : Tuesday, January 28, 2025 at 08:26:28 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&={\frac {3}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 11

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

\[ y = \frac {4}{\left (x -2\right )^{2}} \]

✗ Solution by Mathematica

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

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

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