Internal problem ID [5403]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]
Solve \begin {gather*} \boxed {y^{\prime \prime } y^{\prime }-\left (1+x \right ) x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 51
dsolve(diff(y(x),x$2)*diff(y(x),x)=x*(1+x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \int -\frac {\sqrt {6 x^{3}+9 x^{2}+9 c_{1}}}{3}d x +c_{2} \\ y \relax (x ) = \int \frac {\sqrt {6 x^{3}+9 x^{2}+9 c_{1}}}{3}d x +c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 62.326 (sec). Leaf size: 12885
DSolve[y''[x]*y'[x]==x*(1+x),y[x],x,IncludeSingularSolutions -> True]
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