Internal problem ID [4416]
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: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-3 x^{2} \left (1+y^{2}\right )^{\frac {3}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
dsolve(diff(y(x),x)=3*x^2*(1+y(x)^2)^(3/2),y(x), singsol=all)
\[ c_{1}+x^{3}-\frac {y \relax (x )}{\sqrt {1+y \relax (x )^{2}}} = 0 \]
✓ Solution by Mathematica
Time used: 0.201 (sec). Leaf size: 81
DSolve[y'[x]==3*x^2*(1+y[x]^2)^(3/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \left (x^3+c_1\right )}{\sqrt {\left (x^3-1+c_1\right ) \left (x^3+1+c_1\right )}} \\ y(x)\to \frac {i \left (x^3+c_1\right )}{\sqrt {\left (x^3-1+c_1\right ) \left (x^3+1+c_1\right )}} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}