76.5.27 problem 28

Internal problem ID [17447]
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 2.7 (Substitution Methods). Problems at page 108
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 10:37:56 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 70

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

\begin{align*} y &= -\frac {\sqrt {2}\, \sqrt {\left (x^{2}-1\right ) \left (2 c_{1} -\cos \left (2 x \right )\right )}}{2 x^{2}-2} \\ y &= \frac {\sqrt {2}\, \sqrt {\left (x^{2}-1\right ) \left (2 c_{1} -\cos \left (2 x \right )\right )}}{2 x^{2}-2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.460 (sec). Leaf size: 56

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

\begin{align*} y(x)\to -\frac {\sqrt {-\cos ^2(x)+c_1}}{\sqrt {x^2-1}} \\ y(x)\to \frac {\sqrt {-\cos ^2(x)+c_1}}{\sqrt {x^2-1}} \\ \end{align*}