10.2.4 problem 4

Internal problem ID [1132]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 4
Date solved : Monday, January 27, 2025 at 04:35:09 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 45

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

\begin{align*} y &= -\frac {3}{2}-\frac {\sqrt {4 x^{3}+4 c_1 -4 x +9}}{2} \\ y &= -\frac {3}{2}+\frac {\sqrt {4 x^{3}+4 c_1 -4 x +9}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 59

DSolve[D[y[x],x] == (3*x^2-1)/(3+2*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (-3-\sqrt {4 x^3-4 x+9+4 c_1}\right ) \\ y(x)\to \frac {1}{2} \left (-3+\sqrt {4 x^3-4 x+9+4 c_1}\right ) \\ \end{align*}