Internal problem ID [4428]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (y+1\right ) x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 14
dsolve([diff(y(x),x)=x^2*(1+y(x)),y(0) = 3],y(x), singsol=all)
\[ y \relax (x ) = -1+4 \,{\mathrm e}^{\frac {x^{3}}{3}} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 18
DSolve[{y'[x]==x^2*(1+y[x]),{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 4 e^{\frac {x^3}{3}}-1 \\ \end{align*}