Internal problem ID [4405]
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: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-4 y^{2}+3 y-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve(diff(y(x),x)=4*y(x)^2-3*y(x)+1,y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {7}\, \left (3 \sqrt {7}+7 \tan \left (\frac {\sqrt {7}\, c_{1}}{2}+\frac {\sqrt {7}\, x}{2}\right )\right )}{56} \]
✓ Solution by Mathematica
Time used: 1.677 (sec). Leaf size: 69
DSolve[y'[x]==4*y[x]^2-3*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (3+\sqrt {7} \tan \left (\frac {1}{2} \sqrt {7} (x+c_1)\right )\right ) \\ y(x)\to \frac {1}{8} \left (3-i \sqrt {7}\right ) \\ y(x)\to \frac {1}{8} \left (3+i \sqrt {7}\right ) \\ \end{align*}