50.2.18 problem 4

Internal problem ID [7824]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 4
Date solved : Monday, January 27, 2025 at 03:24:18 PM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 51

dsolve(diff(y(x),x$2)*diff(y(x),x)=x*(1+x),y(x), singsol=all)
 

\begin{align*} y &= -\frac {\left (\int \sqrt {6 x^{3}+9 x^{2}+9 c_{1}}d x \right )}{3}+c_{2} \\ y &= \frac {\left (\int \sqrt {6 x^{3}+9 x^{2}+9 c_{1}}d x \right )}{3}+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 61.314 (sec). Leaf size: 12885

DSolve[D[y[x],{x,2}]*D[y[x],x]==x*(1+x),y[x],x,IncludeSingularSolutions -> True]
 

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