36.1.13 problem 13

Internal problem ID [6268]
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
Date solved : Monday, January 27, 2025 at 01:50:42 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right )^{{3}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x)=3*x^2*(1+y(x)^2)^(3/2),y(x), singsol=all)
 

\[ c_{1} +x^{3}-\frac {y}{\sqrt {1+y^{2}}} = 0 \]

✓ Solution by Mathematica

Time used: 0.260 (sec). Leaf size: 83

DSolve[D[y[x],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 {x^6+2 c_1 x^3-1+c_1{}^2}} \\ y(x)\to \frac {i \left (x^3+c_1\right )}{\sqrt {x^6+2 c_1 x^3-1+c_1{}^2}} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}