36.1.2 problem 2

Internal problem ID [6257]
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
Date solved : Monday, January 27, 2025 at 01:50:16 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=4 y^{2}-3 y+1 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

dsolve(diff(y(x),x)=4*y(x)^2-3*y(x)+1,y(x), singsol=all)
 

\[ y = \frac {3}{8}+\frac {\sqrt {7}\, \tan \left (\frac {\left (x +c_{1} \right ) \sqrt {7}}{2}\right )}{8} \]

✓ Solution by Mathematica

Time used: 1.745 (sec). Leaf size: 69

DSolve[D[y[x],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*}