44.2.47 problem 49

Internal problem ID [6979]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 49
Date solved : Monday, January 27, 2025 at 02:39:36 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} 2 y^{\prime \prime }-3 y^{2}&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.123 (sec). Leaf size: 40

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

\[ y = 4 \operatorname {WeierstrassP}\left (x +\operatorname {RootOf}\left (\operatorname {WeierstrassP}\left (\textit {\_Z} , 0, \operatorname {RootOf}\left (4 \operatorname {WeierstrassPPrime}\left (\operatorname {RootOf}\left (\operatorname {WeierstrassP}\left (\textit {\_Z} , 0, c_{2}\right )\right ), 0, \textit {\_Z}\right )-1\right )\right )\right ), 0, \operatorname {RootOf}\left (4 \operatorname {WeierstrassPPrime}\left (\operatorname {RootOf}\left (\operatorname {WeierstrassP}\left (\textit {\_Z} , 0, c_{2}\right )\right ), 0, \textit {\_Z}\right )-1\right )\right ) \]

✗ Solution by Mathematica

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

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

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