Internal problem ID [6154]
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: 2(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } \left (1+y\right )=-x^{2}+1} \] With initial conditions \begin {align*} [y \left (-1\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 20
dsolve([diff(y(x),x)*(1+y(x))=1-x^2,y(-1) = -2],y(x), singsol=all)
\[ y \left (x \right ) = -1-\frac {\sqrt {-6 x^{3}+18 x +21}}{3} \]
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 28
DSolve[{y'[x]*(1+y[x])==1-x^2,{y[-1]==-2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {-2 x^3+6 x+7}}{\sqrt {3}}-1 \]