76.1.13 problem 13

Internal problem ID [17312]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 09:59:34 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (1-12 x \right ) y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-{\frac {1}{8}} \end{align*}

✓ Solution by Maple

Time used: 0.155 (sec). Leaf size: 16

dsolve([diff(y(x),x)=(1-12*x)*y(x)^2,y(0) = -1/8],y(x), singsol=all)
 

\[ y = \frac {1}{6 x^{2}-x -8} \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 17

DSolve[{D[y[x],x]==(1-12*x)*y[x]^2,{y[0]==-1/8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6 x^2-x-8} \]