76.1.4 problem 4

Internal problem ID [17303]
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 : 4
Date solved : Tuesday, January 28, 2025 at 09:59:09 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 45

dsolve(diff(y(x),x)=(7*x^2-1)/(7+5*y(x)),y(x), singsol=all)
 

\begin{align*} y &= -\frac {7}{5}-\frac {\sqrt {210 x^{3}+90 c_{1} -90 x +441}}{15} \\ y &= -\frac {7}{5}+\frac {\sqrt {210 x^{3}+90 c_{1} -90 x +441}}{15} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 59

DSolve[D[y[x],x]==(7*x^2-1)/(7+5*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{15} \left (-21-\sqrt {210 x^3-90 x+441+90 c_1}\right ) \\ y(x)\to \frac {1}{15} \left (-21+\sqrt {210 x^3-90 x+441+90 c_1}\right ) \\ \end{align*}