Internal problem ID [2101]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\cos \relax (x )-2 x y^{2}}{2 x^{2} y}=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\pi \right ) = \frac {1}{\pi }\right ] \end {align*}
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 14
dsolve([diff(y(x),x)=(cos(x)-2*x*y(x)^2)/(2*x^2*y(x)),y(Pi) = 1/Pi],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {\sin \relax (x )+1}}{x} \]
✓ Solution by Mathematica
Time used: 0.311 (sec). Leaf size: 17
DSolve[{y'[x]==(Cos[x]-2*x*y[x]^2)/(2*x^2*y[x]),{y[Pi]==1/Pi}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {\sin (x)+1}}{x} \\ \end{align*}